Question 1

Solve for $$x$$: $$2(4x + 3) = 7x + 5$$

Accepted Answer

$$x = 1$$

Question 2

Solve for $$x$$: $$\frac{4x}{5} - \frac{x}{10} = \frac{x}{5} + 7$$

Accepted Answer

$$x = 14$$

Question 3

Solve for $$x$$: $$0.15x - 0.03 = 0.2x + 0.12$$

Accepted Answer

$$x = -3$$

Question 4

Solve for $$x$$: $$5(x - 4) + x = 6(x - 2) - 8$$

Accepted Answer

$$x = 8$$

Question 5

A chemist is mixing two solutions. The first solution contains $$0.15x$$ grams of a substance, and the second contains $$0.2x + 0.12$$ grams. If the total after removing $$0.03$$ grams from the first solution equals the second, what is $$x$$?

Accepted Answer

$$x = -3$$

Question 6

A company’s profit is modeled by $$2(4x + 3)$$, where $$x is $$the number of units sold. If the profit must equal $$7x + 5$$, how many units must be sold?

Accepted Answer

$$x = 1$$

Question 7

Which of the following is the correct first step to solve $$5(x - 4) + x = 6(x - 2) - 8$$?

Accepted Answer

Expand both sides: $$5x - 20 + x = 6x - 12 - 8$$

Question 8

If $$\frac{4x}{5} - \frac{x}{10} = \frac{x}{5} + 7$$, what is the value of $$\frac{x}{5}$$?

Accepted Answer

$$\frac{x}{5} = 2.8$$

Question 9

Which equation is equivalent to $$0.15x - 0.03 = 0.2x + 0.12$$ after moving all terms to one side?

Accepted Answer

$$-0.05x - 0.15 = 0$$

Question 10

A real estate agent earns a commission modeled by $$2(4x + 3)$$ dollars, where $$x is $$the number of houses sold. If the agent’s total earnings must match $$7x + 5$$ dollars, how many houses must be sold?

Accepted Answer

$$x = 1$$

Question 11

Which of the following best describes the solution to $$5(x - 4) + x = 6(x - 2) - 8 in $$terms of steps?

Accepted Answer

Expand, collect like terms, isolate $$x$$

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

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