Expressions & one-step equations
Substitute values, tidy expressions, and undo one operation.
In your head, jot if needed · no calculator why?
Opens at level 15. You're level 1. You can read and practice here now.
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
- 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
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
- 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
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
- 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
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
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.
practice
One-step equations
worked example
6x = 66. What is x?
Answer: 11
- Undo × 6 by dividing both sides by 6: x = 66 ÷ 6 = 11.
Evaluate an expression
worked example
Evaluate −9x² − 5x − 5 when x = 3.
Answer: -101
- x² = 3² = 9.
- −9x² = −9 × 9 = −81 and −5x = −5 × 3 = −15.
- Add: −81 − 15 − 5 = −101.
Combine like terms
worked example
Simplify 6(x + 6) + 2x + 7. What is the coefficient of x?
Answer: 8
- Distribute: 6(x + 6) = 6x + 36.
- Collect: 6x + 2x = 8x and 36 + 7 = 43, so it is 8x + 43.
- The coefficient of x is 8.