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Geometry Homework
Algebra 1 Review: Solving Linear Equations

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1.
[tex]\[
\begin{array}{c}
d + 18 = -27 \\
-18 \quad (-18) \\
d = -45
\end{array}
\][/tex]

2. [tex]\( m - 77 = -61 \)[/tex]

3. [tex]\( -12 + a = -36 \)[/tex]

4. [tex]\( 4 - (-x) = 19 \)[/tex]

5. [tex]\( \frac{2}{3} p = 18 \)[/tex]

6. [tex]\( -17y = 91 \)[/tex]

7. [tex]\( 5x = -45 \)[/tex]

8. [tex]\( -\frac{2}{5}d = -10 \)[/tex]

9. [tex]\( b - 10 = 4 \)[/tex]

10. [tex]\( d - 8 = 6 \)[/tex]

11. [tex]\( -28 = p + 21 \)[/tex]

12. [tex]\( -3 - (-g) = -12 \)[/tex]

13. [tex]\( -3x - 7 = 16 \)[/tex]

14. [tex]\( 4h + 5 = 13 \)[/tex]

15. [tex]\( 5d - 6 = d + 10 \)[/tex]

16. [tex]\( 7 + 2(w + 1) = -2w - 11 \)[/tex]

17. [tex]\( -8(4 + 9r) = 7(-2 - 11r) \)[/tex]

18. The difference of the square of [tex]\( y \)[/tex] and twelve is the same as the product of five and [tex]\( x \)[/tex]. Write as an equation.



Answer :

GinnyAnswer
Let's solve each equation step by step.

2. [tex]\( m - 77 = -61 \)[/tex]
[tex]\[ m = -61 + 77 \\ m = 16 \][/tex]

3. [tex]\( -12 + a = -36 \)[/tex]
[tex]\[ a = -36 + 12 \\ a = -24 \][/tex]

4. [tex]\( 4 - (-x) = 19 \)[/tex]
[tex]\[ 4 + x = 19 \implies x = 19 - 4 \\ x = 15 \][/tex]

5. [tex]\( \frac{2}{3}p = 18 \)[/tex]
[tex]\[ p = 18 \times \frac{3}{2} \\ p = 27 \][/tex]

6. [tex]\( -17y = 91 \)[/tex]
[tex]\[ y = \frac{91}{-17} \\ y = -\frac{91}{17} \][/tex]

7. [tex]\( 5x = -45 \)[/tex]
[tex]\[ x = \frac{-45}{5} \\ x = -9 \][/tex]

8. [tex]\( -\frac{2}{5}d = -10 \)[/tex]
[tex]\[ d = -10 \times -\frac{5}{2} \\ d = 25 \][/tex]

9. [tex]\( b - 10 = 4 \)[/tex]
[tex]\[ b = 4 + 10 \\ b = 14 \][/tex]

10. [tex]\( d - 8 = 6 \)[/tex]
[tex]\[ d = 6 + 8 \\ d = 14 \][/tex]

11. [tex]\( -28 = p + 21 \)[/tex]
[tex]\[ p = -28 - 21 \\ p = -49 \][/tex]

12. [tex]\( -3 - (-g) = -12 \)[/tex]
[tex]\[ -3 + g = -12 \\ g = -12 + 3 \\ g = -9 \][/tex]

13. [tex]\( -3x - 7 = 16 \)[/tex]
[tex]\[ -3x = 16 + 7 \implies -3x = 23 \\ x = \frac{23}{-3} \\ x = -\frac{23}{3} \][/tex]

14. [tex]\( 4h + 5 = 13 \)[/tex]
[tex]\[ 4h = 13 - 5 \implies 4h = 8 \\ h = \frac{8}{4} \\ h = 2 \][/tex]

15. [tex]\( 5d - 6 = d + 10 \)[/tex]
[tex]\[ 5d - d = 10 + 6 \implies 4d = 16 \\ d = \frac{16}{4} \\ d = 4 \][/tex]

16. [tex]\( 7 + 2(w + 1) = -2w - 11 \)[/tex]
[tex]\[ 7 + 2w + 2 = -2w - 11 \\ 2w + 2w = -11 - 7 - 2 \\ 4w = -20 \\ w = \frac{-20}{4} \\ w = -5 \][/tex]

17. [tex]\( -8(4 + 9r) = 7(-2 - 11r) \)[/tex]
[tex]\[ -32 - 72r = -14 - 77r \\ 77r - 72r = -14 + 32 \\ 5r = 18 \\ r = \frac{18}{5} \][/tex]

18. The difference of the square of [tex]\( y \)[/tex] and twelve equals the product of five and [tex]\( x \)[/tex].
[tex]\[ y^2 - 12 = 5x \][/tex]

This outlines the detailed solution to each problem with the appropriate equations solved step-by-step.

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