Question

part 3: solving equations
solve each equation.
1 ( y - 5 = 3 )
2 ()
3 ( 63 + x = 90 )
4 ( y + 42 = 180 )
5 ()
6 ( -9p = -45 )
7 ( -4 + 7x = 3 )
8 ( 9 = 6 - (x + 2) )
9 ( 6x + 3 - 8x = 13 )
10 ( 4(x - 2) + 2x = 40 )
11 ( 2x + 7 + 30 + 63 = 180 )
12 ( t + t + 115 = 180 )
13 ( 5x - 6 = 2x - 4 )
14 ( 7x - 4 + 36 = 4x + 47 )
15 ( 4x - 1 + 2x + 1 = 8x - 4 )
16 ( g + 18 = 6g - 2 )
17 ( 3x + 9 + 5x + 9 = 90 )
18 ( 3x - 14 = 2x + 10 )
19 ( 2x + 5x + 5 = 180 )
20 ( x + 27 = 3x - 27 )
21 ( 48 = 2(7x - 1) )
22 ()
23 ( 2(x - 4) = 10 )
24 ( 24 = 2(x - 6) )

Explanation:

Step1: Solve $y-5=3$

Add 5 to both sides:
$y = 3 + 5$
$y=8$

Step2: Solve $63+x=90$

Subtract 63 from both sides:
$x = 90 - 63$
$x=27$

Step3: Solve $y+42=180$

Subtract 42 from both sides:
$y = 180 - 42$
$y=138$

Step4: Solve $\frac{z}{3}=-9$

Multiply by 3 on both sides:
$z = -9 \times 3$
$z=-27$

Step5: Solve $-9p=-45$

Divide by -9 on both sides:
$p = \frac{-45}{-9}$
$p=5$

Step6: Solve $-4+7x=3$

Add 4 to both sides, then divide by 7:
$7x = 3 + 4$
$x = \frac{7}{7}$
$x=1$

Step7: Solve $9=6-(x+2)$

Simplify right side, isolate $x$:
$9 = 6 - x - 2$
$9 = 4 - x$
$x = 4 - 9$
$x=-5$

Step8: Solve $6x+3-8x=13$

Combine like terms, isolate $x$:
$-2x + 3 = 13$
$-2x = 13 - 3$
$x = \frac{10}{-2}$
$x=-5$

Step9: Solve $4(x-2)+2x=40$

Expand, combine like terms, isolate $x$:
$4x - 8 + 2x = 40$
$6x = 40 + 8$
$x = \frac{48}{6}$
$x=8$

Step10: Solve $2x+7+30+63=180$

Combine constants, isolate $x$:
$2x + 100 = 180$
$2x = 180 - 100$
$x = \frac{80}{2}$
$x=40$

Step11: Solve $t+t+115=180$

Combine like terms, isolate $t$:
$2t + 115 = 180$
$2t = 180 - 115$
$t = \frac{65}{2}$
$t=32.5$

Step12: Solve $5x-6=2x-4$

Move $x$ terms to left, constants to right:
$5x - 2x = -4 + 6$
$3x = 2$
$x = \frac{2}{3}$

Step13: Solve $7x-4+36=4x+47$

Combine constants, isolate $x$:
$7x + 32 = 4x + 47$
$7x - 4x = 47 - 32$
$3x = 15$
$x=5$

Step14: Solve $4x-1+2x+1=8x-4$

Combine like terms, isolate $x$:
$6x = 8x - 4$
$6x - 8x = -4$
$-2x = -4$
$x=2$

Step15: Solve $g+18=6g-2$

Move $g$ terms to right, constants to left:
$18 + 2 = 6g - g$
$20 = 5g$
$g = \frac{20}{5}$
$g=4$

Step16: Solve $3x+9+5x+9=90$

Combine like terms, isolate $x$:
$8x + 18 = 90$
$8x = 90 - 18$
$x = \frac{72}{8}$
$x=9$

Step17: Solve $3x-14=2x+10$

Move $x$ terms to left, constants to right:
$3x - 2x = 10 + 14$
$x=24$

Step18: Solve $2x+5x+5=180$

Combine like terms, isolate $x$:
$7x + 5 = 180$
$7x = 180 - 5$
$x = \frac{175}{7}$
$x=25$

Step19: Solve $x+27=3x-27$

Move $x$ terms to right, constants to left:
$27 + 27 = 3x - x$
$54 = 2x$
$x = \frac{54}{2}$
$x=27$

Step20: Solve $48=2(7x-1)$

Expand, isolate $x$:
$48 = 14x - 2$
$14x = 48 + 2$
$x = \frac{50}{14}$
$x=\frac{25}{7}$

Step21: Solve $y+5=3y-5$

Move $y$ terms to right, constants to left:
$5 + 5 = 3y - y$
$10 = 2y$
$y = \frac{10}{2}$
$y=5$

Step22: Solve $2(x-4)=10$

Expand, isolate $x$:
$2x - 8 = 10$
$2x = 10 + 8$
$x = \frac{18}{2}$
$x=9$

Step23: Solve $24=2(x-6)$

Expand, isolate $x$:
$24 = 2x - 12$
$2x = 24 + 12$
$x = \frac{36}{2}$
$x=18$

Answer:

1. $y=8$
2. (equation unclear, solved visible equations)
3. $x=27$
4. $y=138$
5. $z=-27$
6. $p=5$
7. $x=1$
8. $x=-5$
9. $x=-5$
10. $x=8$
11. $x=40$
12. $t=32.5$
13. $x=\frac{2}{3}$
14. $x=5$
15. $x=2$
16. $g=4$
17. $x=9$
18. $x=24$
19. $x=25$
20. $x=27$
21. $x=\frac{25}{7}$
22. $y=5$
23. $x=9$
24. $x=18$