Algebra 1 Common Core Student Edition, Grade 8-9

W hen you solve an equation, you use reasoning to select properties of equality th at

produce sim pler equivalent eq u atio n s u ntil you find a solution. The steps below provide

a general guideline for solving equations.

Co n c ep t Su m m a r y Solving Equations

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Step 1 Use the Distributive P roperty to rem ove any grouping symbols. Use properties

of equality to clear decim als an d fractions.

Step 2 C om bine like term s on each side of th e equation.

Step 3 Use the properties of equality to get th e variable term s on one side of the

equ atio n a n d th e constants on th e other.

Step 4 Use the p roperties of equality to solve for th e variable.

Step 5 C heck your solution in th e original equation.

V J

9 Lesso n Ch eck

Do y o u k n o w H OW?

Solve each equation. Check your answer.

1 .3 x + 4 = 5 x - l 0 2. 5(y - 4) = 7(2y + 1)

3. 2a + 3 = |(6 + 4a) 4. 4x - 5 = 2(2x + 1)


4. Printing Pristine Printing will print business cards
   for $.10 each plus a setup charge of $15. The P rinting
   Place offers business cards for $.15 each w ith a setup
   charge of $10. W hat n u m b e r of business cards costs
   the sam e from either printer?

Do y o u UN DERSTAND? V g J P^ ACtTceS

Vocabulary Match each equation with the appropriate

number of solutions.

6. 3y - 5 = y + 2y — 9

7. 2y + 4 = 2{y + 2)

8. 2y — 4 = 3y — 5

A. infinitely many

B. one solution

C. no solution

9. W riting A stu d e n t solved a n equ atio n a n d found that
   th e variable was elim inated in th e process of solving
   the equation. How would the student know whether
   th e eq u a tio n is a n identity or a n equ atio n with
   no solution?

Pr act i ce an d Pr o b l em - So l v i n g Ex er ci ses

Q Practice Solve each equation. Check your answer.

10. 5x-l=x+15 11. 4p + 2 = 3p — 7


11. 3 + 5q = 9 + 4 q 14. 8 - 2 y = 3 y - 2


12. 2b + 4 = -18 - 9b 17. - 3 c - 12 = -5 + c

MATHEMATICAL

PRACTICES

See Problem 1.

12. 6 m - 2 = 2m + 6

15. 3rc — 5 = 7rc + 11
    18. —n - 24 = 5 - n