Question

name: teresa garza - mejia
week 5 packet
part a: checking solutions by substitution
directions: substitute the given value of x i equal, the value is a solution.

1. $5x - 3 = 4(2x + 3)$; $x = -5$

$3(x - 4) + 2 = 2x - 6$; $x = 2$

Explanation:

For the first equation \( 5x - 3 = 4(2x + 3) \) with \( x = -5 \):

Step1: Substitute \( x = -5 \) into left side

Left side: \( 5(-5) - 3 = -25 - 3 = -28 \)

Step2: Substitute \( x = -5 \) into right side

Right side: \( 4(2(-5) + 3) = 4(-10 + 3) = 4(-7) = -28 \)

Step3: Compare left and right sides

Since \( -28 = -28 \), \( x = -5 \) is a solution.

For the second equation (assuming the first part of the left side is \( 3(x - 4) + 2 = 2x - 6 \) with \( x = 2 \)):

Step1: Substitute \( x = 2 \) into left side

Left side: \( 3(2 - 4) + 2 = 3(-2) + 2 = -6 + 2 = -4 \)

Step2: Substitute \( x = 2 \) into right side

Right side: \( 2(2) - 6 = 4 - 6 = -2 \)

Step3: Compare left and right sides

Since \( -4
eq -2 \), \( x = 2 \) is not a solution.

Answer:

For \( 5x - 3 = 4(2x + 3) \) with \( x = -5 \): \( x = -5 \) is a solution.
For \( 3(x - 4) + 2 = 2x - 6 \) with \( x = 2 \): \( x = 2 \) is not a solution.