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Linear Equations Help

Solve one-step, two-step and multi-step linear equations, including variables on both sides.

A linear equation is solved by getting the variable alone on one side. Whatever you do to one side, do to the other: undo addition and subtraction first, then multiplication and division.

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Example problems & solutions

Q

Solve 3x + 7 = 22

A
  1. Subtract 7 from both sides: 3x = 15.
  2. Divide both sides by 3: x = 5.
  3. Check: 3(5) + 7 = 15 + 7 = 22. ✓

Answer: x = 5

Q

Solve 5x − 4 = 2x + 11

A
  1. Subtract 2x from both sides: 3x − 4 = 11.
  2. Add 4 to both sides: 3x = 15.
  3. Divide by 3: x = 5.
  4. Check: 5(5) − 4 = 21 and 2(5) + 11 = 21. ✓

Answer: x = 5

Q

Solve 2(x + 3) = 4x − 8

A
  1. Distribute the 2: 2x + 6 = 4x − 8.
  2. Subtract 2x from both sides: 6 = 2x − 8.
  3. Add 8 to both sides: 14 = 2x.
  4. Divide by 2: x = 7.
  5. Check: 2(7 + 3) = 20 and 4(7) − 8 = 20. ✓

Answer: x = 7

Q

Solve x/4 + 1 = 6

A
  1. Subtract 1 from both sides: x/4 = 5.
  2. Multiply both sides by 4: x = 20.
  3. Check: 20/4 + 1 = 5 + 1 = 6. ✓

Answer: x = 20

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Frequently asked questions

What is a linear equation?

An equation where the variable is only to the first power, like 3x + 7 = 22. Its graph is a straight line, which is where the name comes from.

What do you do when there are variables on both sides?

Move all the variable terms to one side by adding or subtracting, move the numbers to the other side, then divide by the coefficient.

How can I check my answer?

Substitute your value back into the original equation. If both sides come out equal, the answer is correct.

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