Question 1

Solve for $$x in $$the equation $$7x - 64 - 15x = 4x + 64 + 4x.$$

Accepted Answer

$$x = -8$$

Question 2

After combining like terms, what is the simplified form of $$7x - 64 - 15x = 4x + 64 + 4x$$?

Accepted Answer

$$-8x - 64 = 8x + 64$$

Question 3

What is the next step after simplifying to $$-8x - 64 = 8x + 64$$?

Accepted Answer

Subtract $$8x$$ from both sides

Question 4

What equation do you get after subtracting $$8x$$ from both sides of $$-8x - 64 = 8x + 64$$?

Accepted Answer

$$-16x - 64 = 64$$

Question 5

After adding $$64 to $$both sides of $$-16x - 64 = 64$$, what is the resulting equation?

Accepted Answer

$$-16x = 128$$

Question 6

What is the value of $$x$$ after dividing both sides of $$-16x = 128 by$$ $$-16$$?

Accepted Answer

$$x = -8$$

Question 7

Which of the following steps is necessary to check your solution for $$x in $$the equation $$7x - 64 - 15x = 4x + 64 + 4x$$?

Accepted Answer

Substitute $$x$$ back into the original equation

Question 8

If $$x = -8$$, what is the value of $$7x - 64 - 15x$$?

Accepted Answer

$$-56 - 64 + 120 = 0$$

Question 9

Which property of equality is used when subtracting $$8x$$ from both sides of an equation?

Accepted Answer

Subtraction Property of Equality

Question 10

A chemical reaction is modeled by the equation $$7x - 64 - 15x = 4x + 64 + 4x$$, where $$x$$ represents the amount of a reactant. What is the value of $$x$$ that balances the reaction?

Accepted Answer

$$x = -8$$

Question 11

In a budgeting scenario, if $$7x - 64 - 15x$$ represents expenses and $$4x + 64 + 4x$$ represents income, for what value of $$x$$ are expenses and income equal?

Accepted Answer

$$x = -8$$

Question 12

Which of the following is a correct check for the solution $$x = -8 in $$the equation $$7x - 64 - 15x = 4x + 64 + 4x$$?

Accepted Answer

$$0 = 0$$

Question 13

If you mistakenly add $$8x to $$both sides instead of subtracting, what equation would you get from $$-8x - 64 = 8x + 64$$?

Accepted Answer

$$0 - 64 = 16x + 64$$

Question 14

Which step is necessary to isolate $$x in $$the equation $$-16x = 128$$?

Accepted Answer

Divide both sides by $$-16$$

Solving Linear Equations and Checking Solutions

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