Question

1. $-7(4x - 3)=2x - 9$
2. $4h + 21 = h + 5h + 7$

a. $h = 5$
b. $h = 6$
c. $h = 7$
d. $h = 8$

1. what is the value of $y$ in the equation below?

$4y - 9 + 2y = y + 46$

a. $y = 11$
b. $y = \frac{37}{5}$
c. $y = \frac{55}{7}$
d. $y = \frac{37}{7}$

Explanation:

Problem 5: Solve \(-7(4x - 3)=2x - 9\)

Step 1: Distribute -7

Multiply -7 with each term inside the parentheses: \(-7\times4x + (-7)\times(-3)=2x - 9\)
\(-28x + 21 = 2x - 9\)

Step 2: Move x terms to left

Subtract \(2x\) from both sides: \(-28x - 2x + 21 = 2x - 2x - 9\)
\(-30x + 21 = -9\)

Step 3: Move constant to right

Subtract 21 from both sides: \(-30x + 21 - 21 = -9 - 21\)
\(-30x = -30\)

Step 4: Solve for x

Divide both sides by -30: \(x=\frac{-30}{-30}\)
\(x = 1\)

Step 1: Combine like terms on right

Simplify \(h + 5h\) to \(6h\): \(4h + 21 = 6h + 7\)

Step 2: Move h terms to right

Subtract \(4h\) from both sides: \(4h - 4h + 21 = 6h - 4h + 7\)
\(21 = 2h + 7\)

Step 3: Move constant to left

Subtract 7 from both sides: \(21 - 7 = 2h + 7 - 7\)
\(14 = 2h\)

Step 4: Solve for h

Divide both sides by 2: \(h=\frac{14}{2}\)
\(h = 7\)

Step 1: Combine like terms on left

Simplify \(4y + 2y\) to \(6y\): \(6y - 9 = y + 46\)

Step 2: Move y terms to left

Subtract \(y\) from both sides: \(6y - y - 9 = y - y + 46\)
\(5y - 9 = 46\)

Step 3: Move constant to right

Add 9 to both sides: \(5y - 9 + 9 = 46 + 9\)
\(5y = 55\)

Step 4: Solve for y

Divide both sides by 5: \(y=\frac{55}{5}\)
\(y = 11\)

Answer:

\(x = 1\)

Problem 6: Solve \(4h + 21 = h + 5h + 7\) and choose the correct option