Variables & One-Step Equations · MCAP 6.EE.B.6-7

Learning Goal: Use variables to represent numbers and solve one-step equations of the form x + p = q and px = q.

Vocabulary

variableA letter representing an unknown number you can solve for.

inverse operationThe operation that undoes another: subtraction undoes addition; division undoes multiplication.

isolate the variableGet the variable alone on one side of the equation to find its value.

solutionThe value of the variable that makes the equation true.

What You Need to Know

To solve, do the inverse operation to BOTH sides to keep the equation balanced.
For x + p = q, subtract p from both sides.
For x − p = q, add p to both sides.
For px = q, divide both sides by p.
For x ÷ p = q, multiply both sides by p.
Always check your answer by substituting it back into the original equation.

Worked Example I Do — watch how it works

Solve 8x = 72.

Step 1. The variable is multiplied by 8, so use the inverse: divide both sides by 8.
Step 2. 72 ÷ 8 = 9, so x = 9.
Step 3. Check: 8 × 9 = 72 ✓.

Answer: x = 9

Guided Practice We Do — try it together

1. Solve x + 12 = 19.
💡 Hint: Subtract 12 from both sides to undo the addition.
2. Solve x − 3.5 = 10.
💡 Hint: Add 3.5 to both sides.
3. Solve (1/4)x = 9.
💡 Hint: Multiply both sides by 4 (the inverse of dividing by 4).

Independent Practice You Do — show your work

1. Solve x + 15 = 40.
2. Solve 6x = 54.
3. Solve x − 8 = 11.
4. Solve x/5 = 4.
5. Solve x + 2.5 = 7.

MCAP-Style Practice

Directions: Answer each item the way you would on the MCAP. For selected-response items, fill in the circle (○) next to the correct answer. For constructed-response items, enter your answer and show your work. Every item below assesses standard 6.EE.B.6-7.

Item 1Selected Response6.EE.B.6-7

What is the solution to x + 9 = 21?

Select the correct answer.

○ A. 12○ B. 30○ C. 3○ D. 189

Item 2Selected Response6.EE.B.6-7

Solve 7x = 56.

Select the correct answer.

○ A. 49○ B. 63○ C. 8○ D. 9

Item 3Constructed Response6.EE.B.6-7

Jordan bought packs of pencils with 6 pencils each and got 48 total. Write and solve an equation for the number of packs p.

Enter your answer in the space provided. Show your work.

Enter your answer:

Teacher Answer Key (click to show)

Independent 1	x = 25
Independent 2	x = 9
Independent 3	x = 19
Independent 4	x = 20
Independent 5	x = 4.5
Item 1 · 6.EE.B.6-7	A — Subtract 9 from both sides: 21 − 9 = 12, so x = 12.
Item 2 · 6.EE.B.6-7	C — Divide both sides by 7: 56 ÷ 7 = 8, so x = 8.
Item 3 · 6.EE.B.6-7	6p = 48; p = 8 — 6 pencils per pack times p packs equals 48, so 6p = 48; p = 8.

Neft Teacher · Grade 6 MCAP Mathematics Review · Standard 6.EE.B.6-7