2-1 an d 2 - 2 So l v i n g O n e - a n d Tw o - St ep Eq u a t i o n s
Quick Review
To solve an equation, get the variable by itself on one side
of the equation. You can use properties of equality and
inverse operations to isolate th e variable. For example,
use m ultiplication to u n d o its inverse, division.Ex a m p l e
What is the solution of | + 5 = 8?
|+ 5 - 5 = 8-5 Subtract to undo addition.Simplify.Multiply to undo division.y=6 Simplify.Ex e r c i s e s
Solve each equation. Check your answer.
6. x + 5 = — 2 7. <2-2.5 = 4.5
8. 3b = 42 9. § = 13- 7x — 2 = 22.5^1 COII^1
- 8 + 3 m = - 7 13. —^ + 5 = 11
- Dining Five friends equally split a re sta u ran t bill that
com es to $32.50. How m uch does each pay? - Reasoning Justify each step in solving 4x - 3 = 9.
4 x - 3 + 3 = 9 + 3 J_
4x = 12?
4x _ 12
4 4
X = 32-3 So l v i n g M u l t i - St ep Eq u a t i o n s
Quick Review Ex e r c i s e s
To solve som e equations, you m ay n e e d to com bine like Solve each equation. Check your answer.
term s or use th e D istributive P roperty to clear fractions 16. 7(s - 5) = 42 17. 3fl + 2-5fl=-14_____<< I Q —Ah — 5 + ?h = 1 f) 19 3 4t + 0 68 = 11or decimals.Ex a m p l e
= 2x + f - #?1 O KJ vj X LdU lu 1 J. jtt 1 l/.uU XX- 10 = § — 4 + § 21. Y + 1 = 5
What is the solution of (^12) O O Write an equation to model each situation. Then solve
3 • 12 = 3(2x + f — y j Multiply by 3. the equation.
36 = 6 x + 4 — 2x Simplify.
- Ea r n i n g s You w ork for 4 h on Saturday an d 8 h on
Sunday. You also receive a $50 bonus. You ea rn $164.
36 = 4x + 4 Combine like terms. How m u ch did you ea rn p er hour?
36- 4 = 4x+ 4 - 4 Subtract 4. 23. En t e r t a i n m e n t Online concert tickets cost $37 each,
WtoII X Combine like terms. plus a service charge of $8.50 p e r ticket. The Web
col<N| , 11 31'
Divide each side by 4. site also charges a tran sactio n fee of $14.99 for the
purchase. You paid $242.49. How many tickets did
8 = x Simplify. you buy?
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