Algebra

Linear Equation Solver

Solve linear equations of the form ax + b = c, or more complex equations with variables on both sides (ax + b = cx + d). Full step-by-step working shown — collecting terms, isolating x, and checking the answer.

a (x coefficient)

b (constant left)

c (right-hand side)

Solving: 3x + 5 = 14

Solution

x = 3

How it works

Write the equation
$3x +5 = 14$
We need to solve for x in the equation 3x +5 = 14.
Subtract 5 from both sides
$3x = 14 - 5 = 9$
Subtract 5 from both sides to isolate the x term.
Result:3x = 9
Divide both sides by 3
$x = \frac{9}{3} = 3$
Divide both sides by 3 to find x.
Result:x = 3
Check
$3(3) +5 = 14$
Substitute x = 3 back: 3 × 3 +5 = 14 ✓

The formula

ax + b = c \implies x = \frac{c - b}{a}

a

Coefficient of x

b

Constant on the left-hand side

c

Right-hand side value

Example substitution

3x + 5 = 14 \implies 3x = 9 \implies x = 3

Subtract 5 from both sides: 3x = 9. Divide by 3: x = 3.

Worked examples

Solve 3x + 5 = 14

1
Subtract 5: 3x = 9
2
Divide by 3: x = 3
3
Check: 3(3) + 5 = 14 ✓

Answer: x = 3

Solve 2x − 7 = 11

1
Add 7: 2x = 18
2
Divide by 2: x = 9

Answer: x = 9

Solve 4x + 3 = 2x + 11

1
Collect x terms: 2x + 3 = 11
2
Subtract 3: 2x = 8
3
Divide by 2: x = 4

Answer: x = 4

Frequently asked questions

How do you solve a linear equation?+

Collect all x terms on one side, collect constants on the other, then divide to find x.

How do you solve 3x + 5 = 20?+

Subtract 5: 3x = 15. Divide by 3: x = 5.

How do you solve equations with x on both sides?+

Subtract the smaller x term from both sides first. E.g., 5x + 3 = 2x + 12 → 3x = 9 → x = 3.

How do you check a linear equation answer?+

Substitute your value of x back into the original equation. Both sides should be equal.

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