Intro to Expressions and Equations

Evaluating Expressions

Substitute a value for the variable and compute: evaluate 3x + 2 at x = 4.

Example

Substitute a variable value, then reduce with order of operations.

highlighted = computed this step

Step 1 — Set up

Set up the expression.

3x+2x=43 x+ 2 \quad x= 4
Evaluate 3x + 2 when x = 4.expression3x + 2valuex = 4xxx3 x-tiles plus constant 2The value box tells what x should become.

Step 2 — Substitute

Substitute x = 4: 3(4) + 2.

3(4)+23 ( \hl{4} )+ 2
Replace x with 4: 3(4) + 2.expression3x + 2valuex = 4substitute3(4) + 2xxx3 x-tiles plus constant 2Every x tile is now worth 4.

Step 3 — Multiply first

Multiply first: 3 x 4 = 12.

3×4=123 \times 4 = \hl{12}
Multiply before adding: 3 x 4 = 12.expression3x + 2valuex = 4substitute3(4) + 2multiply first3 x 4 = 12444combine to 123 copies of 4 make 12.

Step 4 — Add

Then add: 12 + 2 = 14.

12+2=1412 + 2 = \hl{14}
Then add the constant: 12 + 2 = 14.expression3x + 2valuex = 4substitute3(4) + 2multiply first3 x 4 = 12444combine to 12add constant12 + 211total 14The constant 2 is added after multiplication.

Step 5 — Result

Read the final result.

1414
The expression value is 14.expression3x + 2valuex = 4substitute3(4) + 2multiply first3 x 4 = 12444combine to 12add constant12 + 211total 14result14So 3x + 2 equals 14 when x = 4.
evaluate-expression To evaluate an algebraic expression: - Replace the variable with its value. - Multiply first (order of operations). - Then add or subtract constants.