PSHS NCE Algebraic Expressions and Simple Equations Reviewer

TEACHER ABI PSHS NCE · QUANTITATIVE ABILITY

Algebraic Expressions and Simple Equations

Translate words into math, understand variables, and solve simple equations by undoing operations.

Grade 6–7 friendlyVariables + equationsRegular practiceQuick Fire + Mastery

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Algebraic Expressions and Simple Equations

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A variable is just a number we do not know yet

If x + 5 = 12, then x is the number that makes the equation true.

x + 5 = 12 → x = 7

Expression: 3x + 4 has no equals sign.
Equation: 3x + 4 = 19 has an equals sign and can be solved.

DO IT FAST

Use TRANSLATE → UNDO → CHECK

1. TRANSLATE: Turn words into a math expression or equation.
2. UNDO: Reverse the operation around the variable.
3. CHECK: Put your answer back into the original equation.

Undo pairs:
+ ↔ −
× ↔ ÷

WORKED EXAMPLES

Six patterns you should recognize

1. Translate words

“Five more than a number n”

n + 5

2. Watch “less than”

“7 less than x”

x − 7

Not 7 − x.

3. Solve addition

x + 8 = 15

Subtract 8 from both sides.

x = 7

4. Solve multiplication

5x = 35

Divide both sides by 5.

x = 7

5. Two-step equation

3x + 4 = 19

Subtract 4: 3x = 15. Divide by 3.

x = 5

6. Story to equation

Four times a number plus 3 equals 27.

4x + 3 = 27

x = 6

TRY WITH ME

Undo one step at a time

2x + 7 = 21

1. Subtract 7 from both sides.
2. Now 2x = 14.
3. Divide both sides by 2.

x = 7
Check: 2(7)+7=21.

COMMON TRAPS

Watch out for these

Changing only one side.
Keep the equation balanced.

Mixing up expressions and equations.
Only equations can be solved.

Reading “less than” in the wrong order.
5 less than x means x−5.

Not checking.
Substitute the answer back in.

REGULAR PRACTICE

Build the skill

These mix translating, evaluating, one-step equations, and simple two-step equations.

QUICK FIRE

Can you undo it fast?

Five short questions. Identify the operation around the variable first.

Question 1 of 5

FRESH MASTERY CHECK

Can you do it without hints?

Score 5/5 to verify this competency. If you miss one, a fresh set will be ready.

NEED HELP?

Equations still feel like a puzzle?

Send Teacher Abi the item that confused you and your result. I can show you what operation to undo first.

Message Teacher Abi

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