Linear Equations

Mathematics — First Preparatory

Linear Equations

Worked examples

Comparison aspect	Main idea	Keywords
Example 1	Solve x + 9 = 15	Solve
Solution	Subtract 9 from both sides to get x = 6. Check: 6 + 9 = 15	SubtractbothsidesCheck
Example 2	Solve 4x − 7 = 13	Solve
Solution	Add 7 to both sides to get 4x = 20 then divide by 4 to get x = 5. Check: 4 × 5 − 7 = 13	bothsidesthendivide
Example 3	Solve 3(x − 2) = 2x + 1	Solve
Solution	Remove the bracket to get 3x − 6 = 2x + 1. Subtract 2x from both sides to get x − 6 = 1 then add 6 to get x = 7. Check: 3(7 − 2) = 15 and 2 × 7 + 1 = 15	RemovebracketSubtractboth
Example 4	Solve (x − 3) ÷ 2 = 5	Solve
Solution	Multiply both sides by 2 to get x − 3 = 10 so x = 13. Check: (13 − 3) ÷ 2 = 5	MultiplybothsidesCheck
Example 5 (the hardest)	Ali has 2 pounds more than three times the money that Hany has. Together they have 26 pounds. Find the money each person has	poundsthreetimesmoney

Solution→Let Hany’s money be h. Then Ali’s money is 3h + 2. The equation is h + 3h + 2 = 26, so 4h = 24 and h = 6. Hany has 6 pounds and Ali has 3 × 6 + 2 = 20 pounds. Check: 6 + 20 = 26.

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