1. Solve the following linear equations: a. x+7=0 C. 2x-7=3 e. 5x-8=2x-2 gy 7(y-2)+21=(2y)(3) b. x+4=9 d. 3x-7=-10 f 10(x+10)-7=13

## Step 1: Solving $x + 7 = 0$<br />### Subtract 7 from both sides of the equation to isolate $x$. $x + 7 - 7 = 0 - 7$ simplifies to $x = -7$.<br />## Step 2: Solving $x + 4 = 9$<br />### Subtract 4 from both sides of the equation to isolate $x$. $x + 4 - 4 = 9 - 4$ simplifies to $x = 5$.<br />## Step 3: Solving $2x - 7 = 3$<br />### Add 7 to both sides: $2x - 7 + 7 = 3 + 7$, simplifying to $2x = 10$. Then, divide both sides by 2: $\frac{2x}{2} = \frac{10}{2}$, resulting in $x = 5$.<br />## Step 4: Solving $3x - 7 = -10$<br />### Add 7 to both sides: $3x - 7 + 7 = -10 + 7$, simplifying to $3x = -3$. Then, divide both sides by 3: $\frac{3x}{3} = \frac{-3}{3}$, resulting in $x = -1$.<br />## Step 5: Solving $5x - 8 = 2x - 2$<br />### Subtract $2x$ from both sides: $5x - 2x - 8 = 2x - 2x - 2$, simplifying to $3x - 8 = -2$. Add 8 to both sides: $3x - 8 + 8 = -2 + 8$, simplifying to $3x = 6$. Divide both sides by 3: $\frac{3x}{3} = \frac{6}{3}$, resulting in $x = 2$.<br />## Step 6: Solving $10(x + 10) - 7 = 13$<br />### Add 7 to both sides: $10(x + 10) - 7 + 7 = 13 + 7$, simplifying to $10(x + 10) = 20$. Divide both sides by 10: $\frac{10(x + 10)}{10} = \frac{20}{10}$, simplifying to $x + 10 = 2$. Subtract 10 from both sides: $x + 10 - 10 = 2 - 10$, resulting in $x = -8$.<br />## Step 7: Solving $7(y - 2) + 21 = (2y)(3)$<br />### Distribute the 7 and simplify the right side: $7y - 14 + 21 = 6y$, which simplifies to $7y + 7 = 6y$. Subtract $6y$ from both sides: $7y - 6y + 7 = 6y - 6y$, simplifying to $y + 7 = 0$. Subtract 7 from both sides: $y + 7 - 7 = 0 - 7$, resulting in $y = -7$.