58
Final review: solving equations
Textbook, pp. 231–232
GoalReview solving linear equations and solving word problems with equations.
New words
equation · tenglamaroot (solution) · ildizcoefficient · koeffitsiyentchecking · tekshirish
Explanation
To solve an equation we first remove brackets, move the unknown terms to one side and the numbers to the other (changing their signs), combine like terms and divide by the coefficient. In an equation with fractional coefficients, multiply both sides by the LCM of the denominators to remove the fractions. We always check the solution in the original equation. In a word problem we denote the unknown by a letter and form an equation from the condition: “three times a number minus 7 equals 20” gives 3x − 7 = 20.
Worked examples
2(x + 3) = 18: x + 3 = 9, so x = 6. Check: 2 · 9 = 18.
−3x = 21: x = 21 : (−3) = −7.
Class activity
“Make an equation”: pairs create equations for each other (for example “I multiplied my number by 4 and added 5 and got 25”). The partner solves it, finds the number and checks.
Practice
1
Solve 5x − 8 = 2x + 7.
5
2
Solve x/3 + x/2 = 15.
18
3
Three times a number minus 7 gives 20. Find the number.
9
4
Why should a solution be checked in the original equation?
There may be an arithmetic or sign mistake; if a true equality results, the solution is correct.