Equations with brackets, decimals and fractions · Usually met around P6
Equations with brackets and like terms
Join like terms; a bracket: divide first or open it.
How to do it
Method
Join like terms; a bracket: divide first or open it
3(x + 4) = 27 → x + 4 = 9 → x = 5
Another way
Open the bracket first
3x + 12 = 27 → 3x = 15 → x = 5
In full
First tidy the equation into “a number of x = a number”, then find x. Like terms join together: 3x + 2x = 5x, 7x − 4x = 3x. With a bracket there are two ways: for 3(x + 4) = 27, divide both sides by 3 to get x + 4 = 9, then take 4 from both sides, x = 5; or open the bracket first — the 3 multiplies everything inside: 3x + 12 = 27, take 12 from both sides, 3x = 15, then divide by 3, x = 5. Both ways give the same answer. Last, put the answer back into the equation to check: 3 × (5 + 4) = 27.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Solve 4(x + 11) = 84. x = □
Show the answer and working
Answer: 10
Divide both sides by 4: x + 11 = 21; take 11 from both sides: x = 10.
Example 2
Solve 5x + 4x + 24 = 87. x = □
Show the answer and working
Answer: 7
Join: 9x + 24 = 87; take 24 from both sides: 9x = 63; x = 7.
Example 3
x = 3 solves 4(x + 6) = 36.
True or false?
Show the answer and working
Answer: True
Check by putting it in: with x = 3, 4 × (3 + 6) = 36, so the answer is x = 3.
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