Top 33 How To Solve 4M 4 4M Best 233 Answer

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Subtract 4m 4 m from 4m 4 m . Subtract 4 4 from 0 0 . Since −4≠0 – 4 ≠ 0 , there are no solutions.A multi-step equation is an equation that takes two or more steps to solve. These problems can have a mix of addition, subtraction, multiplication, or division. We also might have to combine like terms or use the distributive property to properly solve our equations. So get your mathematical toolbox out!

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What is multi-step equations?

A multi-step equation is an equation that takes two or more steps to solve. These problems can have a mix of addition, subtraction, multiplication, or division. We also might have to combine like terms or use the distributive property to properly solve our equations. So get your mathematical toolbox out!

What is P 4 math?

Explanation: 4P4 means the number of ways (permutations) of arranging 4 items from a collection of 4 items.

How do you solve 4x 28?

Algebra Examples

Divide each term in 4x=28 4 x = 28 by 4 . Cancel the common factor of 4 . Cancel the common factor. Divide x x by 1 1 .

Solve 4m-4=4m

Solve for m 4m-4=4m | Mathway

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Solve for m 4m-4=4m | Mathway

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Table of Contents:

What is a multi-step equation

Examples of multi-step equations

How to solve multi-step equations

Multi-step equations with fractions

Multi-step equations with distributive property

Multi-step equation word problems

Keys to Remember Solving Multi-Step Equations

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Solving Multi-Step Equations: Review and Examples

Whether you’re new to solving multi-step equations or simply studying before that big chapter test, Albert has you covered!

This blog post will guide you through defining multi-step equations, examples of multi-step equations, and how to solve multi-step equations (including problems with fractions and words). Let’s go!

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What is a multi-step equation?

Remember, an equation is a mathematical sentence that uses an equal sign, = , to show that two expressions are equal.

We began our study of solving equations with one-step equations, then we moved on to two-step equations. (Check out those links if you need a quick refresher!)

Now we are moving to multi-step equations. A multi-step equation is an equation that takes two or more steps to solve. These problems can have a mix of addition, subtraction, multiplication, or division. We also might have to combine like terms or use the distributive property to properly solve our equations.

So get your mathematical toolbox out! You never know what you might see in a multi-step equation!

Examples of multi-step equations

Multi-step equations are a wide-ranging category of equations. Some can be very simple, while others become more complex. Never fear! We’re going to show you many examples of multi-step equations and how to solve these important aspects of Algebra 1.

Here are some examples of multi-step equations:

5x + 10 = 3x + 12

8y – 3 – 2y = 5

4(3m – 2) = 16

5x – 10 + 5 = 20 – 5x

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How to solve multi-step equations

Remember, an equation is solved when we have isolated the variable and found a value that makes the equation true. In order to solve equations, we use inverse operations to help us isolate the variable.

\text{Addition} \leftrightarrow \text{Subtraction}

\text{Multiplication} \leftrightarrow \text{Division}

Order of Operations

Another mathematical concept that will help when solving multi-step equations is the Order of Operations. To use the order of operations, we must first do any operations inside grouping symbols (parentheses, brackets, etc), then exponents, then multiplication or division (whatever comes first, left to right), then finally addition or subtraction (whatever comes first, left to right). You can remember this by the acronym, PEMDAS.

Additionally, we may have to combine like terms on either side of the equation to help solve these equations. Eventually, you will create a one- or two-step equation that you will be able to solve similarly to previous problems!

Here is an example of a multi-step equation with variables on both sides:

Solve for x in the following equation:

8x – 10 = 4x + 2 Original equation

Since there are variables on both sides, we must eliminate the variable from one side first. I suggest moving the 4x first, as to not create a negative.

8x – 4x – 10 = 4x – 4x + 2 Subtract 4x from each side 4x – 10 = 2 Simplify

Now we are back to a basic two-step equation.

4x – 10 + 10 = 2 + 10 Add 10 from each side 4x = 12 Simplify \dfrac{4x}{4} = \dfrac{12}{4} Divide each side by 4 x = 3 Simplify

To check you answer, you can simplify substitute 3 into the variable to see if the equation is true:

8x – 10 = 4x + 2 Original equation 8(3) – 10 = 4(3) + 2 Substitute 24 – 10 = 12 + 2 Simplify 14 = 14 \checkmark Answer confirmed

Thus, x = 3 is the correct solution.

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Below is a short video from Mike DeVor showing more examples of solving multi-step equations:

Now that we have been introduced to Multi-Step Equations, let’s get those brain gears in motion and look at some more challenging examples!

Multi-step equations with fractions

When dealing with an equation with more than one fraction, the easiest way to solve the equation is by finding the Least Common Denominator. The least common denominator is the smallest number that can be a common denominator for a set of fractions.

Once we find the least common denominator, we will multiply each term by this value to eliminate the fraction. Here is an example of a multi-step equation with fractions:

Solve for y in the following equation:

\dfrac{5y}{6} – \dfrac{1}{4} = \dfrac{3y}{4} + \dfrac{1}{2}

The denominators above are 2, 4, 6 , therefore the least common denominator for these numbers is 12 . So we will multiply each term by 12 .

12 \cdot \dfrac{5y}{6} – 12 \cdot \dfrac{1}{4} = 12 \cdot \dfrac{3y}{4} + 12 \cdot \dfrac{1}{2} Multiply each term by 12 \dfrac{60y}{6} – \dfrac{12}{4} = \dfrac{36y}{4} + \dfrac{12}{2} Result of multiplication 10y – 3 = 9y + 6 Simplify 10y – 9y – 3 = 9y – 9y + 6 Subtract 9y from each side y – 3 = 6 Simplify y – 3 + 3 = 6 + 3 Add 3 to each side y = 9 Simplify

To check your answer, you can substitute 9 into the variable to see if the equation is true:

\dfrac{5y}{6} – \dfrac{1}{4} = \dfrac{3y}{4} + \dfrac{1}{2} Original equation 10y – 3 = 9y + 6 Simplified equation (all terms multiplied by 12 ) 10 \cdot 9 – 3 = 9 \cdot 9 + 6 Substitute 90 – 3 = 81 + 6 Simplify 87 = 87 \checkmark Answer confirmed

Therefore, y = 9 is the correct solution.

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Multi-step equations with distributive property

Example 1

Solve for z in the following equation:

2(3z – 4) = 10 Original equation 2(3z) – 2(4) = 10 Distributive Property 6z – 8 = 10 Simplify 6z – 8 + 8 = 10 + 8 Add 8 to each side 6z = 18 Simplify \dfrac{6z}{6} = \dfrac{18}{6} Divide each side by 6 z = 3 Simplify

To check you answer, you can substitute 3 into the variable to see if the equation is true:

2(3z – 4) = 10 Original equation 2(3 \cdot 3 – 4) = 10 Substitute 2(9 – 4) = 10 Simplify 2(5) = 10 Simplify 10 = 10 \checkmark Answer confirmed

Thus, z = 3 is the correct solution.

Example 2

Solve for m in the following equation:

3(m + 3) – 4 = 2(m – 2) Original equation 3(m) + 3(3) – 4 = 2(m) – 2(2) Distributive Property 3m + 9 – 4 = 2m – 4 Simplify 3m + 5 = 2m – 4 Combine like terms 3m – 2m + 5 = 2m – 2m – 4 Subtract 2m from each side m + 5 = – 4 Simplify m + 5 – 5 = – 4 – 5 Subtract 5 from each side m = -9 Simplify

To check you answer, you can simplify substitute -9 into the variable to see if the equation is true:

3(m + 3) – 4 = 2(m – 2) Original equation 3(-9 + 3) – 4 = 2(-9 – 2) Substitute 3(-6) – 4 = 2(-11) Simplify -18 – 4 = -22 Combine like terms -22 = -22 \checkmark Answer confirmed

Thus, m = -9 is the correct solution.

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Multi-step equation word problems

Example 1

Rob owns a coffee shop and is looking at finding a new coffee distributor for his beans. Distributor A sells their beans for \$5 a pound, plus a flat \$10 shipping fee. Distributor B sells their beans for \$2 a pound, plus \$1 per pound for shipping, plus a \$40 processing fee. What amount of pounds, p , would be a breakeven point for the two companies?

Solution

First, let’s create an equation for the situation:

5p + 10 = 2p + 1p + 40 Original equation 5p + 10 = 3p + 40 Combine like terms 5p -3p + 10 = 3p – 3p + 40 Subtract 3p from each side 2p + 10 = 40 Simplify 2p + 10 – 10 = 40 – 10 Subtract 10 from each side 2p = 30 Simplify \dfrac{2p}{2} = \dfrac{30}{2} Divide each side by 2 p = 15 Simplify

To check you answer, you can simplify substitute 15 into the variable to see if the equation is true:

5p + 10 = 2p + 1p + 40 Original equation 5(15) + 10 = 2(15) + 1(15) + 40 Substitute 75 + 10 = 30 + 15 + 40 Simplify 85 = 85 \checkmark Answer confirmed

Therefore, the breakeven point for Distributor A and Distributor B would be 15 pounds.

Example 2

Sam goes to a bookstore with a coupon for \$5 off a book. The coupon is allowed to be used as many times as Sam wants. He ends up buying three books that all cost the same amount of money. The total cost for the books was \$45 . How much did each book cost, c , before the coupon was applied?

Solution

First, let’s set up an equation that models the situation:

3(c – 5) = 45

Since each book costs the same amount, we denote this amount by the variable, c . Then we applied the \$5 coupon to each book, and finally, we will multiply the cost of each book after the coupon by 3 .

Now, simply solve for c like any other multi-step equation:

3(c) – 3(5) = 45 Distribute the 3 3c – 15 = 45 Simplify 3c – 15 + 15 = 45 + 15 Add 15 to both sides 3c = 60 Simplify \dfrac{3c}{3} = \dfrac{60}{3} Divide both sides by 3 c = 20 Solved

Therefore, each book cost \$20 before the coupon was applied.

Keys to Remember: Solving Multi-Step Equations

A multi-step equation is an equation that requires two or more steps to solve.

When solving: remember whatever you do to one side, you must do to the other.

To solve multi-step equations with fractions, you can multiply each term by the least common denominator to eliminate the fractions first.

To check the solution, simply substitute the value into the variable to see if the equation is true.

You can model real-life situations with an equation and solve for a correct solution.

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How to solve 4m 4 4m?

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Solution for 4m-4=4m equation:

Simplifying 4m + -4 = 4m Reorder the terms: -4 + 4m = 4m Add ‘-4m’ to each side of the equation. -4 + 4m + -4m = 4m + -4m Combine like terms: 4m + -4m = 0 -4 + 0 = 4m + -4m -4 = 4m + -4m Combine like terms: 4m + -4m = 0 -4 = 0 Solving -4 = 0 Couldn’t find a variable to solve for. This equation is invalid, the left and right sides are not equal, therefore there is no solution.

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So you have finished reading the how to solve 4m 4 4m topic article, if you find this article useful, please share it. Thank you very much. See more: 4m-4=4m answer, 4m-4=4m step by step, 5p-14=8p+4, p 4 p, -8=-(x+4), p-1=5p+3p-8 step by step, 24a-22=-4(1-6a), 6) p – 1 = 5p + 3p – 8

Top 33 How To Solve 4M 4 4M Best 233 Answer

What is multi-step equations?

What is P 4 math?

How do you solve 4x 28?

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Solving Multi-Step Equations: Review and Examples

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