Question

solve multi-step equations (continued)
intervention
lesson k32
solve each equation for x.

1. $-4x + 3x + 2 = 6$
2. $6 - x - 3x = -10$
3. $3 + 3x + 5 + 4x = 29$
4. $4x + 6 = x + 12$
5. $6x - 6 = 3(x + 2)$
6. $5x + 8 = x + 2x - 2$
7. $3(x - 6) + 9x = 30$
8. $4(2x + 3x + 8) = 72$
9. $-3(3x - 5) + 4x = 30$
10. $7x - 18 = 3x + 6$
11. $2x + 4 = x + 3(x + 2)$
12. $5x - 8 = x + 2(x - 2)$
13. $2(6x - 4) + 8 = 36$
14. $\frac{1}{2}(x - 8) = 14$
15. $3(1.5x - 4) = 6$
16. $\frac{1}{4}(x + 8) = x + 2$
17. $4.2(x - 2) = x + 2$
18. $2.3(2x + 4) = 0.6x + 10$
19. $5(3x + 2x + 10) = 150$
20. $12 + 4x - 2 = 3(x + 6) - x$
21. $16 + 8(x + 3) - 2x = 82$
22. $3(5x + 6x - 10) = 5(2x + 40)$
23. $4 + 7(x + 4) = 2(x + 4) + x$
24. $\frac{1}{2}(4x + 16 + 6x) = 17x + 2$
25. reasoning what is the first step when solving the equation $8(6x - 4) + 10 = 74$?

Explanation:

Problem 6

Step1: Combine like terms
$-x + 2 = 6$
Step2: Subtract 2
$-x = 4$
Step3: Multiply by -1
$x=-4$

Problem7

Step1: Combine like terms
$6 - 4x = -10$
Step2: Subtract6
$-4x=-16$
Step3: Divide by -4
$x=4$

Problem8

Step1: Combine like terms
$7x + 8 =29$
Step2: Subtract8
$7x=21$
Step3: Divide by7
$x=3$

Problem9

Step1: Subtract $x$
$3x +6=12$
Step2: Subtract6
$3x=6$
Step3: Divide by3
$x=2$

Problem10

Step1: Distribute RHS
$6x-6=3x+6$
Step2: Subtract $3x$
$3x-6=6$
Step3: Add6
$3x=12$
Step4: Divide by3
$x=4$

Problem11

Step1: Combine RHS terms
$5x+8=3x-2$
Step2: Subtract $3x$
$2x+8=-2$
Step3: Subtract8
$2x=-10$
Step4: Divide by2
$x=-5$

Problem12

Step1: Distribute
$3x-18+9x=30$
Step2: Combine terms
$12x-18=30$
Step3: Add18
$12x=48$
Step4: Divide by12
$x=4$

Problem13

Step1: Combine inside parentheses
$4(5x+8)=72$
Step2: Divide by4
$5x+8=18$
Step3: Subtract8
$5x=10$
Step4: Divide by5
$x=2$

Problem14

Step1: Distribute
$-9x+15+4x=30$
Step2: Combine terms
$-5x+15=30$
Step3: Subtract15
$-5x=15$
Step4: Divide by-5
$x=-3$

Problem15

Step1: Subtract $3x$
$4x-18=6$
Step2: Add18
$4x=24$
Step3: Divide by4
$x=6$

Problem16

Step1: Distribute RHS
$2x+4=x+3x+6$
Step2: Combine RHS
$2x+4=4x+6$
Step3: Subtract $2x$
$4=2x+6$
Step4: Subtract6
$-2=2x$
Step5: Divide by2
$x=-1$

Problem17

Step1: Distribute RHS
$5x-8=x+2x-4$
Step2: Combine RHS
$5x-8=3x-4$
Step3: Subtract $3x$
$2x-8=-4$
Step4: Add8
$2x=4$
Step5: Divide by2
$x=1$

Problem18 (assumed $2(6x-4)+8=32$)

Step1: Distribute
$12x-8+8=32$
Step2: Simplify
$12x=32$ → correction: if $2(6x-4)+8=32$, $12x-8+8=32$ → $12x=32$? No, likely $2(6x-4)+8=32$ → $12x-8+8=32$ → $12x=32$ wrong; correct typo: $2(6x-4)+8=32$ → $12x=32$ no, maybe $2(6x-4)+8=32$ → $12x=32$ no—actual: $2(6x-4)+8=32$ → $12x=32$ error, but if $2(6x-4)+8=32$ → $12x=32$ no, so assume $2(6x-4)+8=32$ → $12x=32$ no, but answer $x=3$ (check: $2(18-4)+8=28+8=36$—so original problem likely $2(6x-4)+8=36$ → $12x=36$ → $x=3$)

Problem19

Step1: Multiply by2
$x-8=28$
Step2: Add8
$x=36$

Problem20

Step1: Divide by3
$1.5x-4=2$
Step2: Add4
$1.5x=6$
Step3: Divide by1.5
$x=4$

Problem21

Step1: Multiply by4
$x+8=4x+8$
Step2: Subtract $x$
$8=3x+8$
Step3: Subtract8
$0=3x$
Step4: Divide by3
$x=0$

Problem22

Step1: Distribute
$4.2x-8.4=x+2$
Step2: Subtract $x$
$3.2x-8.4=2$
Step3: Add8.4
$3.2x=10.4$
Step4: Divide by3.2
$x=2$

Problem23

Step1: Distribute
$4.6x+9.2=0.6x+10$
Step2: Subtract0.6x
$4x+9.2=10$
Step3: Subtract9.2
$4x=0.8$
Step4: Divide by4
$x=0.2$? Correction: $2.3*2x=4.6x$, $2.3*4=9.2$ → $4.6x+9.2=0.6x+10$ → $4x=0.8$ → $x=0.2$ (typo earlier: $x=0.2$)

Problem24

Step1: Combine inside
$5(5x+10)=150$
Step2: Divide by5
$5x+10=30$
Step3: Subtract10
$5x=20$
Step4: Divide by5
$x=4$

Problem25

Step1: Simplify LHS/RHS
$10+4x=3x+18-x$ → $10+4x=2x+18$
Step2: Subtract2x
$10+2x=18$
Step3: Subtract10
$2x=8$
Step4: Divide by2
$x=4$ correction: $12+4x-2=3(x+6)-x$ → $10+4x=3x+18-x$ → $10+4x=2x+18$ → $2x=8$ → $x=4$

Problem26

Step1: Distribute
$16+8x+24-2x=82$
Step2: Combine terms
$6x+40=82$
Step3: Subtract40
$6x=42$
Step4: Divide by6
$x=7$

Problem27

Step1: Combine inside
$3(11x-10)=5(2x+40)$
Step2: Distribute
$33x-30=10x+200$
Step3: Subtract10x
$23x-30=200$
Step4: Add30
$23x=230$
Step5: Divide by23
$x=10$

Problem28

Step1: Distribute
$4+7x+28=2x+8+x$
Step2: Combine terms
$7x+32=3x+8$
Step3: Subtract3x
$4x+32=8$
Step4: Subtract32
$4x=-24$
Step5: Divide by4
$x=-6$ correction: $4+7(x+4)=2(x+4)+x$ → $4+7x+28=2x+8+x$ → $7x+32=3x+8$ → $4x=-24$ → $x=-6$

Problem29

Step1: Combine inside
$\frac{1}{2}(10x+16)=17x+2$
Step2: Multiply by2
$10x+16=34x+4$
Step3: Subtract10x
$16=24x+4$
Step4: Subtract4
$12=24x$
Step5: Divide by24
$x=0.5$ correction: $\frac{1}{2}(4x+16+6x)=17x+2$ → $\frac{1}{2}(10x+16)=17x+2$ → $5x+8=17x+2$ → $-12x=-6$ → $x=0.5$

Problem30

First step: Distribute the 8 to the terms inside the parentheses $(6x-4)$.

Answer:

1. $x=-4$
2. $x=4$
3. $x=3$
4. $x=2$
5. $x=4$
6. $x=-5$
7. $x=4$
8. $x=2$
9. $x=-3$
10. $x=6$
11. $x=-1$
12. $x=1$
13. $x=3$ (assuming typo: $2(6x-4)+8=32$)
14. $x=36$
15. $x=4$
16. $x=0$
17. $x=2$
18. $x=0.8$
19. $x=4$
20. $x=2$
21. $x=7$
22. $x=10$
23. $x=-4$
24. $x=0.4$
25. Distribute 8 to $(6x-4)$