How many linear equations practice problems are on this page?

16, each with the full worked solution shown — no sign-up and nothing hidden behind a paywall.

Math Foundations · Algebra Building Blocks

Linear Equations — Practice Problems and Worked Solutions

Keep an equation balanced while isolating the unknown.

The formulas you need here

Solving a linear equation

a x + b = c ⟹ x = \frac{c - b}{a}

What it says: Undo what was done to x, in reverse order, doing the same to both sides.
When to reach for it: One unknown, appearing only to the first power.
Watch out: Whatever you do to one side must happen to the whole other side, not just its first term.

3 x + 4 = 19 \Rightarrow x = \frac{19 - 4}{3} = 5

Subtract, then divide — the reverse of multiply, then add.

16 worked problems

Every step is generated and checked by a computer algebra system.

1.
Solve the equation for x.
$x + 3 = 8$
Answer: $5$
Step-by-step solution
1. $Undo operations while keeping both sides equal.$
2. $x = 5$
3. $Check: both sides equal 8.$
2.
Solve the equation for x.
$2 x = 14$
Answer: $7$
Step-by-step solution
1. $Undo operations while keeping both sides equal.$
2. $x = 7$
3. $Check: both sides equal 14.$
3.
Solve the equation for x.
$3 x - 4 = 11$
Answer: $5$
Step-by-step solution
1. $Undo operations while keeping both sides equal.$
2. $x = 5$
3. $Check: both sides equal 11.$
4.
Solve the equation for x.
$2 x + 6 = 16$
Answer: $5$
Step-by-step solution
1. $Undo operations while keeping both sides equal.$
2. $x = 5$
3. $Check: both sides equal 16.$
5.
Solve the equation for x.
$5 - 2 x = - 9$
Answer: $7$
Step-by-step solution
1. $Undo operations while keeping both sides equal.$
2. $x = 7$
3. $Check: both sides equal - 9.$
6.
Solve the equation for x.
$3 x - 2 = 2 x + 9$
Answer: $11$
Step-by-step solution
1. $Undo operations while keeping both sides equal.$
2. $x = 11$
3. $Check: both sides equal 31.$
7.
Solve the equation for x.
$x + 5 = 12$
Answer: $7$
Step-by-step solution
1. $Undo operations while keeping both sides equal.$
2. $x = 7$
3. $Check: both sides equal 12.$
8.
Solve the equation for x.
$3 x = 18$
Answer: $6$
Step-by-step solution
1. $Undo operations while keeping both sides equal.$
2. $x = 6$
3. $Check: both sides equal 18.$
9.
Solve the equation for x.
$2 x - 5 = 9$
Answer: $7$
Step-by-step solution
1. $Undo operations while keeping both sides equal.$
2. $x = 7$
3. $Check: both sides equal 9.$
10.
Solve the equation for x.
$3 x + 3 = 15$
Answer: $4$
Step-by-step solution
1. $Undo operations while keeping both sides equal.$
2. $x = 4$
3. $Check: both sides equal 15.$
11.
Solve the equation for x.
$7 - 3 x = - 8$
Answer: $5$
Step-by-step solution
1. $Undo operations while keeping both sides equal.$
2. $x = 5$
3. $Check: both sides equal - 8.$
12.
Solve the equation for x.
$4 x - 2 = 3 x + 7$
Answer: $9$
Step-by-step solution
1. $Undo operations while keeping both sides equal.$
2. $x = 9$
3. $Check: both sides equal 34.$
13.
Solve the equation for x.
$x - 4 = 3$
Answer: $7$
Step-by-step solution
1. $Undo operations while keeping both sides equal.$
2. $x = 7$
3. $Check: both sides equal 3.$
14.
Solve the equation for x.
$5 x = 35$
Answer: $7$
Step-by-step solution
1. $Undo operations while keeping both sides equal.$
2. $x = 7$
3. $Check: both sides equal 35.$
15.
Solve the equation for x.
$2 x + 7 = 1$
Answer: $- 3$
Step-by-step solution
1. $Undo operations while keeping both sides equal.$
2. $x = - 3$
3. $Check: both sides equal 1.$
16.
Solve the equation for x.
$6 - x = 2$
Answer: $4$
Step-by-step solution
1. $Undo operations while keeping both sides equal.$
2. $x = 4$
3. $Check: both sides equal 2.$

The formulas you need here

Solving a linear equation

16 worked problems

More from Math Foundations