Solving 2x + 3 = 11 step by step — free printable diagram

How to solve 2x + 3 = 11

2x + 3 = 11 is a linear equation: it asks which single number x makes the two sides equal. Undo the 3 first and then the 2, and the answer is x = 4. Substituting back gives 2 × 4 + 3 = 11, which checks.

Equation

2x + 3 = 11

Step 1 — subtract 3 from both sides

2x = 8

Step 2 — divide both sides by 2

x = 4

Solution

x = 4

Check

2 × 4 + 3 = 11

• Whatever you do to one side of an equation you must do to the other. Subtracting 3 from both sides keeps the two sides equal and leaves 2x on its own: 11 − 3 = 8, so 2x = 8.
• Then divide both sides by 2, because 2x means 2 × x and division undoes multiplication: 8 ÷ 2 = 4, so x = 4.
• The order matters. Work the operations off in reverse: the 3 was added last, so it comes off first, and the × 2 comes off second. Dividing by 2 before subtracting 3 would mean dividing the 3 as well.
• Always check by substituting the answer into the ORIGINAL equation, not into a line you worked out: 2 × 4 = 8, and 8 + 3 = 11. If the two sides match, x = 4 is right.
• Subtracting and dividing are called inverse operations, and this undo-in-reverse method solves every equation of this shape, whatever the numbers.