Question

19.. 43 = 8w + 11

1. \\(\frac{h}{-3} + 7 = 15\\)
2. 4(x + 3) = -36
3. -4w + 3 = w - 27
4. 9(g - 4) = 2g - 1
5. 2(4 + 2k) + 10 = k

Explanation:

Problem 19: \( 43 = 8w + 11 \)

Step 1: Subtract 11 from both sides

To isolate the term with \( w \), we subtract 11 from both sides of the equation.
\( 43 - 11 = 8w + 11 - 11 \)
\( 32 = 8w \)

Step 2: Divide both sides by 8

To solve for \( w \), we divide both sides of the equation by 8.
\( \frac{32}{8} = \frac{8w}{8} \)
\( 4 = w \)

Step 1: Subtract 7 from both sides

To isolate the term with \( h \), we subtract 7 from both sides of the equation.
\( \frac{h}{-3} + 7 - 7 = 15 - 7 \)
\( \frac{h}{-3} = 8 \)

Step 2: Multiply both sides by -3

To solve for \( h \), we multiply both sides of the equation by -3.
\( \frac{h}{-3} \times (-3) = 8 \times (-3) \)
\( h = -24 \)

Step 1: Divide both sides by 4

To isolate the term with \( x \), we divide both sides of the equation by 4.
\( \frac{4(x + 3)}{4} = \frac{-36}{4} \)
\( x + 3 = -9 \)

Step 2: Subtract 3 from both sides

To solve for \( x \), we subtract 3 from both sides of the equation.
\( x + 3 - 3 = -9 - 3 \)
\( x = -12 \)

Answer:

\( w = 4 \)

Problem 20: \( \frac{h}{-3} + 7 = 15 \)