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High School Math : How to solve two-step equations with integers in pre-algebra

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Example Question #51 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for if

-3(x-17)=84

Possible Answers:

x=30

x=-11

x=-15

x=10

Correct answer:

x=-11

Explanation:

The problem above is a two-step algebra problem with distribution.

To solve you must first distribute the outside of the parentheses into both of the numbers inside by multiplying.

Remember when you distribute a negative that both of the numbers inside the parentheses are being multiplied by a negative number so they must flip signs.

Our problem now looks like -3x+51=84

Then we must get our variable, , by itself.

To do this we must subtract the number, , from each side of the equation:

-3x+51-51=84-51

Perform the math so our equation looks like -3x=33

Then we divide each side of the equation by the number that is in front of to get by itself $\frac{-3x}{-3}=\frac{33}{-3}$

Solve the math to find the answer x=-11 .

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Example Question #52 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for if x+91=5x-29 .

Possible Answers:

x=30

x=25

x=19

x=120

Correct answer:

x=30

Explanation:

When there are variables and numbers on each side of the equation, to solve we must mathematically move the variables onto one side and the numbers onto the other.

To do this we put all of the variables on the right side of the equal sign by subtracting from the each side of the equation to have

x-x+91=5x-x-29

When adding or subtracting variables you only add or subtract the numbers in front of the variables. If there is no number the number value is .

Perform the math 91=4x-29

Then to get all of the integers to the left side we will add to each side of the equation to have

91+29=4x-29+29

Perform the math

120=4x

At this point we must divide each side of the equation by the number that is in front of to get by itself

$\frac{120}{4}=\frac{4x}{4}$

Perform the math to find the answer x=30 .

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Example Question #53 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for if

$\frac{x}{8}-17=32$

Possible Answers:

x=472

x=392

x=71

x=294

Correct answer:

x=392

Explanation:

To perform a two-step algebra problem with addition and division we must remove the numbers from so it is by itself on one side of the equation.

To do this we first look to see if a number is being added or subtracted from .

In this case a number is being subtracted so we must add the number, , to each side of the equation.

$\frac{x}{8}-17+17=32+17$

Perform the math so our equation looks like

$\frac{x}{8}=49$

Then we multiply each side of the equation by the number that is under to get by itself

$(8)\cdot \frac{x}{8}=49\cdot (8)$

Perform the math to find the answer x=392 .

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Example Question #54 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for if

9x+22=67

Possible Answers:

x=42

x=12

x=5

x=71

Correct answer:

x=5

Explanation:

To perform a two-step algebra problem with addition and multiplication we must remove the numbers from so it is by itself on one side of the equation.

To do this we first look to see if a number is being added or subtracted from .

In this case a number is being added so we must subtract the number, , from each side of the equation

9x+22-22=67-22

Perform the math so our equation looks like

9x=45

Then we divide each side of the equation by the number that is in front of to get by itself

$\frac{9x}{9}=\frac{45}{9}$

Perform the math to find the answer x=5 .

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Example Question #55 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for if

-2(x-15)=60

Possible Answers:

x=-15

x=15

x=30

x=-30

Correct answer:

x=-15

Explanation:

The problem above is a two-step algebra problem with distribution.

To solve you must first distribute the outside of the parentheses to both of the numbers inside the parentheses by multiplying.

Remember when you distribute a negative that both of the numbers inside the parentheses are being multiplied by a negative number so they must flip signs.

Our problem now looks like

-2x+30=60

Then we must get our variable, , by itself.

To do this we must subtract the number, , from each side of the equation

-2x+30-30=60-30

Perform the math so our equation looks like

-2x=30

Then we divide each side of the equation by the number that is in front of to get by itself

$\frac{-2x}{-2}=\frac{30}{-2}$

Solve the math to find the answer x=-15

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Example Question #56 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for if

x+57=2x-9

Possible Answers:

x=70

x=58

x=31

x=66

Correct answer:

x=66

Explanation:

When there are variables and numbers on each side of the equation, to solve we must mathematically move the variables onto one side and the numbers onto the other.

To do this we put all of the variables on the right side of the equal sign by subtracting from each side of the equation to have

x-x+57=2x-x-9

When adding or subtracting variables you only add or subtract the numbers in front of the variables. If there is no number the number value is .

Perform the math.

57=x-9

Then to get all of the integers to the left side we will add to both sides of the equation to have

57+9=x-9+9

Perform the math.

66=x

The answer is x=66 .

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Example Question #57 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for if

$\frac{x}{7}+71=144$

Possible Answers:

x=444

x=511

x=72

Correct answer:

x=511

Explanation:

To perform a two-step algebra problem with addition and division we must remove the numbers from so it is by itself on one side of the equation.

To do this we first look to see if a number is being added or subtracted from .

In this case a number is being added so we must subtract the number, , from each side of the equation

$\frac{x}{7}+71-71=144-71$

Perform the math so our equation looks like

$\frac{x}{7}=73$

Then we multiply each side of the equation by the number that is in front of to get by itself

$(7)\cdot \frac{x}{7}=(73)\cdot (7)$

Perform the math to find the answer

x=511

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Example Question #58 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for if

$\frac{x}{3}-21=90$

Possible Answers:

x=144

x=113

x=257

x=333

Correct answer:

x=333

Explanation:

To perform a two-step algebra problem with addition and division we must remove the numbers from so it is by itself on one side of the equation.

To do this we first look to see if a number is being added to or subtracted from .

In this case a number is being subtracted so we must add the number, , to each side of the equation.

$\frac{x}{3}-21+21=90+21$

Perform the math so our equation looks like

$\frac{x}{3}=111$

Then we multiply each side of the equation by the number that is under to get by itself

$(3)\cdot \frac{x}{3}=(111)\cdot (3)$

Perform the math to find the answer.

x=333

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Example Question #59 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for if

7(x-5)=14

Possible Answers:

x=7

x=5

x=8

x=9

Correct answer:

x=7

Explanation:

The problem above is a two-step algebra problem with distribution.

To solve you must first distribute the outside of the parentheses into both of the numbers inside the parentheses by multiplying to get

7x-35=14

Then we must get our variable, , by itself.

To do this we must add the number to each side of the equation

7x-35+35=14+35

Perform the math so our equation looks like

7x=49

Then we divide each side of the equation by the number that is in front of to get by itself

$\frac{7x}{7}=\frac{49}{7}$

Perform the math to find the answer

x=7

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Example Question #60 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for if

$7x^{2}=112$

Possible Answers:

$x=\pm8$

$x=\pm6$

$x=\pm7$

$x=\pm4$

Correct answer:

$x=\pm4$

Explanation:

To solve for we must get all of the numbers on the other side of the equation of .

When solving a simple two-step equation we must remove the numbers that are interacting with in this order: Addition/Subtraction, Multiplication/Division, Exponents.

To do this in a problem where is being multiplied by a number, we must divide both sides of the equation by the number.

In this case the number is so we divide each side of the equation by to make it look like this

$\frac{7x^{2}}{7}=\frac{112}{7}$

Our new problem will look like this

$x^{2}=16$

We then must solve the polynomial.

To solve an equation with we must take the square root of each side of the equation to get by itself.

Doing this makes our problem look like

$\sqrt{x^{2}}=\sqrt{16}$

Then we perform the square root to get the answer

$x=\pm4$

Remember that $-4^{2}$ can also equal so our answer will be both positive and negative.

The final answer is $x=\pm4$ .

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High School Math : How to solve two-step equations with integers in pre-algebra

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #51 : How To Solve Two Step Equations With Integers In Pre Algebra

Example Question #52 : How To Solve Two Step Equations With Integers In Pre Algebra

Example Question #53 : How To Solve Two Step Equations With Integers In Pre Algebra

Example Question #54 : How To Solve Two Step Equations With Integers In Pre Algebra

Example Question #55 : How To Solve Two Step Equations With Integers In Pre Algebra

Example Question #56 : How To Solve Two Step Equations With Integers In Pre Algebra

Example Question #57 : How To Solve Two Step Equations With Integers In Pre Algebra

Example Question #58 : How To Solve Two Step Equations With Integers In Pre Algebra

Example Question #59 : How To Solve Two Step Equations With Integers In Pre Algebra

Example Question #60 : How To Solve Two Step Equations With Integers In Pre Algebra

All High School Math Resources

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