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

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Question

Solve for if

$7x^{2}=112$

Answer

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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Question

Solve for if

Answer

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

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.

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

Perform the math.

The answer is .

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Question

Solve for if .

Answer

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

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

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

Perform the math

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 .

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Question

Solve for if

$4x^{2}=324$

Answer

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

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

$\frac{4x^{2}}{4}=\frac{324}{4}$

Our simplified equation becomes

$x^{2}=81$

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 $\sqrt{x^{2}}=\sqrt{81}$

Then we perform the square root to get the answer $x=\pm9$

Remember that $-9^{2}$ can also equal so our answer will be both positive and negative.

The final answer looks like $x=\pm9$ .

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Question

Solve for :

Answer

$\frac{0}{3}=\frac{3n}{3}$

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Question

Solve for .

Answer

$\frac{32x}{32}=\frac{64}{32}$

$x=\frac{64}{32}$

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Question

Solve for when

Answer

To solve for , begin by subtracting from both sides of the equation:

Then divide both sides by :

$\frac{5x}{5}=\frac{40}{5}$

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Question

Solve for when $\frac{x}{4}+16=48$

Answer

To solve for , begin by subtracting from both sides of the equation:

$\frac{x}{4}+16-16=48-16$

$\frac{x}{4}=32$

Then multiply both sides by :

$\frac{x}{4}\cdot 4=32\cdot 4$

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Question

Solve for when

Answer

To solve for , first add to both sides of the equation:

Then divide each side of the equation by :

$\frac{7x}{7}=\frac{84}{7}$

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Question

Solve for when $\frac{x}{13}-8=6$

Answer

To solve for , first add to both sides of the equation:

$\frac{x}{13}-8+8=6+8$

$\frac{x}{13}=14$

Then multiply both sides of the equation by :

$\frac{x}{13}\cdot 13=14\cdot 13$

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Question

Solve for when

Answer

To solve for , first subtract from both sides of the equation:

Then divide both sides of the equation by :

$\frac{8x}{8}=\frac{64}{8}$

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Question

Solve for when $\frac{x}{9}+71=89$

Answer

To solve for , first subtract from both sides of the equation:

$\frac{x}{9}+71-71=89-71$

$\frac{x}{9}=18$

Then multiply each side of the equation by :

$\frac{x}{9}\cdot 9=18\cdot 9$

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Question

Solve for when $\frac{x}{4}-25=5$

Answer

To solve for , begin by adding to both sides of the equation:

$\frac{x}{4}-25+25=5+25$

$\frac{x}{4}=30$

Then multiply both sides by :

$\frac{x}{4}\cdot 4=30\cdot 4$

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Question

Solve for when

Answer

To solve for , begin by adding to both sides of the equation:

Then divide both sides of the equation by :

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

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Question

Solve for if,

Answer

To solve for , first distribute the outside the parentheses to both values inside the parentheses:

Then subtract from both sides of the equation:

Then divide each side of the equation by :

$\frac{4x}{4}=\frac{40}{4}$

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Question

Solve for when

Answer

To solve for , first distribute the outside the parentheses to both values inside the parentheses:

Then add to both sides of the equation:

Then divide both sides by :

$\frac{8x}{8}=\frac{96}{8}$

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Question

Solve for when

Answer

To solve for , first distribute the outside the parentheses to both values inside the parentheses:

Then add to both sides of the equation:

Then divide both sides of the equation by :

$\frac{-3x}{-3}=\frac{60}{-3}$

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Question

Solve for when

Answer

To solve for , first distribute the outside the parentheses to both values inside the parentheses:

Then subtract from both sides of the equation:

Then divide both sides by :

$\frac{-6x}{-6}=\frac{12}{-6}$

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Question

Solve for when

Answer

When there are variables on both sides of the equation, it is easiest to move them to the same side. Move all variables to the left side of the equation by subtracting from each side:

Then subtract from each side of the equation:

Then divide each side by :

$\frac{-2x}{-2}=\frac{22}{-2}$

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Question

Solve for when

Answer

When there are variables on both sides of the equation, it is easiest to move them to the same side. Move all variables to the right side of the equation by subtracting from each side:

Then add to both sides of the equation:

Then divide each side of the equation by :

$\frac{36}{6}=\frac{6x}{6}$

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