22 problems graded by difficulty (★ easy, ★★ medium, ★★★ hard). Try first, without looking at the solutions!
2 Subtracting first ★★★
Solve \(3x - 4 = 11\).
3 Division inside ★★★
Solve \(\dfrac{x}{4} + 3 = 8\).
4 Larger numbers ★★★
Solve \(7x + 2 = 51\).
5 Divide then subtract ★★★
Solve \(\dfrac{x}{3} - 2 = 4\).
6 Is it a solution? ★★★
Decide whether each value is a solution of \(6x - 5 = 19\).
- \(x = 4\)
- \(x = 3\)
7 Two ways to start ★★★
To solve \(3x + 6 = 21\), Mia subtracts 6 first. Dev says it is also fine to divide everything by 3 first. Who can be right? Solve the equation both ways.
8 Parentheses first ★★★
Solve \(4(x + 3) = 44\).
9 A difference in parentheses ★★★
Solve \(3(x - 5) = 21\) by dividing first.
10 Decimal coefficients ★★★
Solve \(2.5x + 1.5 = 11.5\).
11 Gym membership ★★★
A gym charges a $20 joining fee plus $15 each month. Lena has paid $155 in total. Write an equation and find how many months she has been a member.
12 Taxi ride ★★★
A taxi charges $3.50 plus $2 per mile. A ride cost $17.50. How many miles was the ride?
13 Fraction coefficient ★★★
Solve \(\dfrac{2}{3}x + 4 = 10\).
14 Find the error ★★★
Jo solved \(5x + 10 = 45\) like this: “\(5x = 35\), so \(x = 35 - 5 = 30\).” Find his mistake and give the correct solution.
15 Fractions on both terms ★★★
Solve \(\dfrac{x}{2} - \dfrac{3}{4} = \dfrac{5}{4}\).
16 Fraction times a sum ★★★
Solve \(\dfrac{3}{4}(x - 8) = 9\).
17 Temperature conversion ★★★
The formula \(F = 1.8C + 32\) converts degrees Celsius to degrees Fahrenheit. A thermometer shows 77 °F. Find the temperature in °C.
18 Notebooks and a pen ★★★
Sam buys 3 identical notebooks and one pen that costs $4.25. He pays $13.25 in all. Write an equation and find the price of one notebook.
19 Arithmetic versus algebra ★★★
I think of a number, multiply it by 6, and subtract 9. The result is 33.
- Find the number by working backward with arithmetic only.
- Write an equation and solve it.
- Compare the two solutions.
20 Perimeter of a rectangle ★★★
A rectangle is 9 cm wide. Its length \(x\) is unknown and its perimeter is 50 cm.
Use \(2(9 + x) = 50\) to find the length, then compute the area.
21 Negative coefficients ★★★
Solve each equation and check.
- \(-3x + 7 = -11\)
- \(\dfrac{x}{-2} + 1 = 5\)
22 Create a word problem ★★★
Write a word problem (with your own context) that matches the equation \(4x + 6 = 30\), then solve it.
Test yourself: quick challenge for Grade 7
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