Question

directions: solve each equation for the variable. show all work.

1. -4x + 7 = 11
2. 17 = 5y - 3
3. -4 = 2p + 10
4. -(x - 10) = 7
5. -2(y + 5) = -6
6. 8 = 4(x - 2) + 4
7. x - 4 + 2x = 14
8. 4(y + 1) = -8
9. -2(d + 6) = -10

Explanation:

Problem 1: $-4x + 7 = 11$

Step 1: Subtract 7 from both sides

To isolate the term with \( x \), we subtract 7 from both sides of the equation.
\( -4x + 7 - 7 = 11 - 7 \)
Simplifying, we get:
\( -4x = 4 \)

Step 2: Divide by -4

To solve for \( x \), we divide both sides by -4.
\( \frac{-4x}{-4} = \frac{4}{-4} \)
Simplifying, we find:
\( x = -1 \)

Problem 2: $17 = 5y - 3$

Step 1: Add 3 to both sides

To isolate the term with \( y \), we add 3 to both sides.
\( 17 + 3 = 5y - 3 + 3 \)
Simplifying, we get:
\( 20 = 5y \)

Step 2: Divide by 5

To solve for \( y \), we divide both sides by 5.
\( \frac{20}{5} = \frac{5y}{5} \)
Simplifying, we find:
\( y = 4 \)

Problem 3: $-4 = 2p + 10$

Step 1: Subtract 10 from both sides

To isolate the term with \( p \), we subtract 10 from both sides.
\( -4 - 10 = 2p + 10 - 10 \)
Simplifying, we get:
\( -14 = 2p \)

Step 2: Divide by 2

To solve for \( p \), we divide both sides by 2.
\( \frac{-14}{2} = \frac{2p}{2} \)
Simplifying, we find:
\( p = -7 \)

Problem 4: $-(x - 10) = 7$

Answer:

s:

1. \( \boldsymbol{x = -1} \)
2. \( \boldsymbol{y = 4} \)
3. \( \boldsymbol{p = -7} \)
4. \( \boldsymbol{x = 3} \)
5. \( \boldsymbol{y = -2} \)
6. \( \boldsymbol{x = 3} \)
7. \( \boldsymbol{x = 6} \)
8. \( \boldsymbol{y = -3} \)
9. \( \boldsymbol{d = -1} \)