Question

1. check. substitute the solution into the equation for x.

$3(x - 7) = 2x + 4$
$3(\underline{\quad} - 7) = 2(\underline{\quad}) + 4$
$3(\underline{\quad}) = \underline{\quad} + 4$
$\underline{\quad} = \underline{\quad}$
solve $2(x + 40 + 7x) = 4x + 20$ for $x$.

1. $2(x + 40 + 7x) = 4x + 20$

combine like terms inside the parentheses.
$2(\underline{\quad}x + 40) = 4x + 20$
$2(\underline{\quad}x) + 2(\underline{\quad}) = 4x + 20$
use the distributive property.
$\underline{\quad}x + \underline{\quad} = 4x + 20$
$16x + 80 - \underline{\quad}x = 4x + 20 - \underline{\quad}x$
subtract $4x$ from both sides.
$\underline{\quad}x + 80 - \underline{\quad} = 20 - \underline{\quad}$
subtract $80$ from both sides.
$\underline{\quad}x = \underline{\quad}$
divide both sides by 12.
$x = \underline{\quad}$

1. the solution is $x = \underline{\quad}$.

Explanation:

Problem 3 (Equation \(3(x - 7) = 2x + 4\))

Step1: Solve for \(x\) first

Expand left side: \(3x - 21 = 2x + 4\). Subtract \(2x\): \(x - 21 = 4\). Add 21: \(x = 25\)

Step2: Substitute \(x=25\) into equation

Left side: \(3(25 - 7) = 3(18) = 54\). Right side: \(2(25) + 4 = 50 + 4 = 54\). Both sides equal.

Problem 4-5 (Equation \(2(x + 40 + 7x) = 4x + 20\))

Step1: Combine like terms inside parentheses

\(x + 7x = 8x\), so \(2(8x + 40) = 4x + 20\)

Step2: Apply Distributive Property

\(2(8x) + 2(40) = 16x + 80 = 4x + 20\)

Step3: Subtract \(4x\) from both sides

\(16x + 80 - 4x = 4x + 20 - 4x\) → \(12x + 80 = 20\)

Step4: Subtract 80 from both sides

\(12x + 80 - 80 = 20 - 80\) → \(12x = -60\)

Step5: Divide by 12

\(x = \frac{-60}{12} = -5\)

Answer:

• For equation \(3(x - 7) = 2x + 4\): \(x = 25\)
• For equation \(2(x + 40 + 7x) = 4x + 20\): \(x = -5\)