courses › Pre-Algebra

Expressions & one-step equations

level 15 course

Substitute values, tidy expressions, and undo one operation.

In your head, jot if needed · no calculator why?

Opens at level 15.

Builds on: Order of operations (not open yet)

the lesson

The idea, the techniques and a tip for each skill, right here. The Learn page adds worked examples for every skill and untimed practice.

Read the lesson · about 3 minutes

The idea

A letter like x stands for a number you don't know yet. 3x means 3 × x, and x² means x × x.

Three moves cover this course. To evaluate an expression, put the number in for x and follow the order of operations. To simplify, multiply out brackets and combine like terms, the terms with the same letter part: 3x and −5x combine to −2x. To solve a one-step equation, undo the one thing done to x, on both sides.

Techniques

Undo the operation

x has one number added, taken away, multiplied or divided.

Name what was done to x: add, subtract, multiply or divide by a number.
Do the opposite to both sides.
Check by putting your answer back in.

worked example

Example: x − 9 = −4. What is x?

Undo − 9 by adding 9 to both sides.
x = −4 + 9 = 5.
Check: 5 − 9 = −4.

Answer: 5

Substitute in brackets

Evaluating an expression at a given x, especially a negative one.

Write the value in brackets wherever x appears.
In the x² term, square the x first, then multiply by the number in front.
Add the terms, keeping each sign.

worked example

Example: Evaluate 2x² − 3x + 4 when x = −2.

x² = (−2) × (−2) = 4.
2x² = 2 × 4 = 8, and −3x = −3 × (−2) = 6.
8 + 6 + 4 = 18.

Answer: 18

Multiply out, then collect

Simplifying an expression with a bracket and loose terms.

Multiply every term in the bracket by the number outside, sign included.
Add up the numbers in front of the x terms.
Add up the plain numbers.

worked example

Example: Simplify 4(x − 3) − 6x + 5. What is the constant term?

Multiply out: 4x − 12 − 6x + 5.
x terms: 4x − 6x gives −2x.
Numbers: −12 + 5 = −7.
So it is −2x − 7.

Answer: −7

Tips by skill

TipOne-step equations: Ask what was done to x, then do the opposite to both sides.
TipEvaluate an expression: Put the value in brackets, square before multiplying, and keep every sign.
TipCombine like terms: Multiply out the bracket first, sign included. Then add the x numbers together and the plain numbers together.

Watch out for

Subtracting instead of dividing. 7x means 7 × x, so undo it by dividing both sides by 7.
Squaring 3x instead of x. In 3x² only the x is squared; then multiply by 3.
Forgetting that a negative number squared is positive: (−2)² is 4.
Multiplying only the first term in the bracket, or losing the minus in front of a term like −5x.

skills · practice stats

From rounds of this course only: box, review and test-out answers are left out. Once a skill has 40 tries, it compares your first 20 tries with your last 20.

One-step equations par 6 s not tried yet
worked example
6x = 66. What is x?

Answer: 11
1. Undo × 6 by dividing both sides by 6: x = 66 ÷ 6 = 11.
Evaluate an expression par 11 s not tried yet
worked example
Evaluate −9x² − 5x − 5 when x = 3.

Answer: -101
1. x² = 3² = 9.
2. −9x² = −9 × 9 = −81 and −5x = −5 × 3 = −15.
3. Add: −81 − 15 − 5 = −101.
Combine like terms par 12 s not tried yet
worked example
Simplify 6(x + 6) + 2x + 7. What is the coefficient of x?

Answer: 8
1. Distribute: 6(x + 6) = 6x + 36.
2. Collect: 6x + 2x = 8x and 36 + 7 = 43, so it is 8x + 43.
3. The coefficient of x is 8.

rest ladder

Win 3 of your last 4 rounds and the course rests. A win is 90% right, within 2× the round's par. Pass the review when it comes back and the next rest is longer.

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