Solving Two-Step Equations: math test, Grade 7 – download the PDF

1 Solve four equations / 4 pts

Solve each equation. Show your steps.

1. \(3x + 8 = 29\)
2. \(\dfrac{x}{6} - 1 = 3\)
3. \(5x - 12 = 38\)
4. \(2(x + 9) = 40\)

2 Checking values / 3 pts

1. Is \(x = 8\) a solution of \(7x - 6 = 50\)?
2. Is \(x = -3\) a solution of \(2x + 11 = 4\)?
3. Find the solution of \(2x + 11 = 4\).

3 Rational coefficients / 3 pts

Solve each equation.

1. \(\dfrac{3}{5}x + 2 = 11\)
2. \(0.4x - 1.2 = 2\)

4 Saving for a bike / 4 pts

Nora has $12 in her account and saves $7.50 each week. She wants to reach $57. Let \(w\) be the number of weeks.

1. Write an equation.
2. Solve it.
3. Answer with a sentence.

5 Garden fence / 3 pts

A rectangular garden is 6 m wide and \(x\) meters long. The perimeter is 34 m.

1. Write an equation of the form \(p(x + q) = r\).
2. Solve it and answer with a sentence.

6 Number puzzle / 3 pts

I think of a number, multiply it by 4 and add 9. The result is 53.

1. Find the number with arithmetic only.
2. Find it with an equation.