Question 1

Solve for $$x in $$the equation $$3(x + 2) = 15.$$

Accepted Answer

$$x = 3$$

Question 2

Which of the following is the correct first step to solve $$-3(4x - 1) = 45$$?

Accepted Answer

$$-12x + 3 = 45 ($$Distribute $$-3 to $$both terms inside the parentheses)

Question 3

Solve for $$x in $$the equation $$-3(4x - 1) = 45.$$

Accepted Answer

$$x = 4$$

Question 4

Given $$2 - 4(3 + 4x) = 54$$, what is the value of $$x$$?

Accepted Answer

$$x = 4$$

Question 5

Which property is used when you rewrite $$2 - 4(3 + 4x) as$$ $$2 - 12 - 16x$$?

Accepted Answer

Distributive Property

Question 6

Solve for $$x in $$the equation $$5 - (1 - 7x) + 6x = 251.$$

Accepted Answer

$$x = 30$$

Question 7

Which of the following is the correct simplification of $$5 - (1 - 7x) + 6x$$?

Accepted Answer

$$5 - 1 + 7x + 6x ($$Distribute the negative sign)

Question 8

Solve for $$x in $$the equation $$-3 + 5x = 4x - 10.$$

Accepted Answer

$$x = -7$$

Question 9

A chemist needs to prepare a solution by mixing two chemicals. If the equation for the amount of chemical $$x$$ needed is $$3(x + 2) = 15$$, how much of chemical $$x$$ should be used?

Accepted Answer

$$x = 3$$ units

Question 10

If $$-3 + 5x = 4x - 10$$ represents the balance between expenses and income in a business, what value of $$x$$ will make the business break even?

Accepted Answer

$$x = -7$$

Question 11

Which step is necessary to isolate $$x in $$the equation $$-3 + 5x = 4x - 10$$?

Accepted Answer

Subtract $$4x$$ from both sides

Question 12

What is the solution to $$2 - 4(3 + 4x) = 54$$ after distributing and combining like terms?

Accepted Answer

$$-10 - 16x = 54$$

Step-by-Step Guidance for Solving Linear Equations (Intermediate Algebra)

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