Linear equations: solved examples

Worked examples of linear equations, from easy to hard, with every step written out. Try each one yourself first, then check the working.

✓ Every answer here is computed and checked by the math engine

Easy

Example 1. Solve $x + 19 = 26$ .
1. Subtract 19 from both sides. $x = 26 - 19 = 7$
Answer: $x = 7$
Example 2. Solve $x + 3 = 4$ .
1. Subtract 3 from both sides. $x = 4 - 3 = 1$
Answer: $x = 1$
Example 3. Solve $2x = 20$ .
1. Divide both sides by 2. $x = \frac{20}{2} = 10$
Answer: $x = 10$

Example 4. Solve $-4x + 18 = 14$ .
1. Subtract 18 from both sides. $-4x = 14 - 18 = -4$
2. Divide by -4. $x = \frac{-4}{-4} = 1$
Answer: $x = 1$
Example 5. Solve $-4x - 16 = 24$ .
1. Subtract -16 from both sides. $-4x = 24 - (-16) = 40$
2. Divide by -4. $x = \frac{40}{-4} = -10$
Answer: $x = -10$
Example 6. Solve $8x - 20 = 28$ .
1. Subtract -20 from both sides. $8x = 28 - (-20) = 48$
2. Divide by 8. $x = \frac{48}{8} = 6$
Answer: $x = 6$

Example 7. Solve $-4x = 8x - 12$ .
1. Collect x terms on the left. $-12x = -12$
2. Move the constant and divide. $-12x = -12 \;\Rightarrow\; x = 1$
Answer: $x = 1$
Example 8. Solve $-4x + 14 = -7x - 16$ .
1. Collect x terms on the left. $3x + 14 = -16$
2. Move the constant and divide. $3x = -30 \;\Rightarrow\; x = -10$
Answer: $x = -10$
Example 9. Solve $8x + 19 = -9x + 121$ .
1. Collect x terms on the left. $17x + 19 = 121$
2. Move the constant and divide. $17x = 102 \;\Rightarrow\; x = 6$
Answer: $x = 6$

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