Intro to Expressions and Equations

Two-Step Equations

Solve using two inverse operations: 2x + 3 = 11 → subtract 3, then divide by 2 → x = 4.

two-step-equation To solve a two-step equation: - First undo addition or subtraction. - Then undo multiplication or division. - Verify by substituting the solution back.

Example

Use inverse operations on both sides until the variable is alone.

highlighted = computed this step

Step 1 — Set up

Set up the expression.

2x+3=112 x+ 3 = 11
Start balanced: 2x + 3 = 11.2x + 311=The two sides start equal.

Step 2 — Subtract from both sides

Subtract 3 from both sides.

2x+3−3=11−32 x+ 3 - \hl{3} = 11 - \hl{3}
Undo + 3 by subtracting 3 from both sides.2x + 3 - 311 - 3=subtract 3subtract 3Same subtraction keeps the balance level.

Step 3 — Simplify

After subtracting, the equation is 2x = 8.

2x=82 x = \hl{8}
11 - 3 = 8, so 2x = 8.2x8=The constant is gone; the variable term is alone.

Step 4 — Divide both sides

Divide both sides by 2: 2/2 and 8/2.

22x=82\hlmath{\frac{2}{2}} x = \hlmath{\frac{8}{2}}
Undo multiply by 2: divide both sides by 2.left sideright sidex4x4=2 equal x groups8 split into 2 equal groupsEach group is 8/2 = 4, so x = 4.

Step 5 — Simplify

Simplify to solve: x = 4.

x=4x = \hl{4}
After dividing by 2, x = 4.x4=One x matches one equal share.

Step 6 — Check

Check: 2 x 4 + 3 = 11.

2×4+3=112 \times 4 + 3 = \hl{11}
Check: 2 x 4 + 3 = 11.2 x 4 + 311=Substitute the solution back into the original equation.

Step 7 — Result

Read the final result.

x=4x = 4
Solution: x = 4.x4=The variable is isolated.