Equations and Inequalities: math test, Grade 6 – download the PDF

1 Solve the equations / 4 pts

1. \(x + 13 = 40\)
2. \(9y = 72\)
3. \(m - 6.5 = 3.5\)
4. \(\dfrac{k}{7} = 8\)

2 Is it a solution? / 3 pts

1. Is 5 a solution of \(4x = 20\)?
2. Is 11 a solution of \(x + 7 = 17\)?
3. Is 24 a solution of \(\dfrac{z}{6} = 4\)?

3 Equations from stories / 4 pts

1. A baker sold 36 muffins in the morning. By closing time she had sold 91 muffins. Write an equation and find how many she sold after the morning.
2. Four friends share a $52 bill equally. Write an equation and find what each pays.

4 Inequalities / 4 pts

1. Solve \(y - 7 < 5\).
2. Solve \(6w \leq 54\).
3. Draw the solutions of \(w \leq 9\) on a number line from 0 to 12.
4. Which of 7, 9 and 10 are solutions of \(w \leq 9\)?

5 The museum / 3 pts

A museum allows at most 120 visitors inside at once. There are already 78 people inside, and \(v\) more want to enter.

1. Write an inequality.
2. Solve it.
3. Can 45 more people enter? Explain.

6 The flower bed / 2 pts

A rectangular flower bed is 9 feet long and has an area of 63 square feet. Write an equation for its width \(w\) and solve it. Give the answer in feet and in meters (1 ft is about 0.3 m).