Question

1. determine the value of a in each of the following equations if the solution to each of the equations is x = 4.

a) 2x + a = 15
b) 5(3x - a) = 2x + 7
c) ax + 5 - 2x - 7 = 14

Explanation:

Step1: Substitute $x=4$ into equation a)

$2(4) + A = 15$

Step2: Simplify and solve for A

$8 + A = 15$
$A = 15 - 8$

Step3: Substitute $x=4$ into equation b)

$5(3(4) - A) = 2(4) + 7$

Step4: Simplify and solve for A

$5(12 - A) = 8 + 7$
$60 - 5A = 15$
$-5A = 15 - 60$
$-5A = -45$
$A = \frac{-45}{-5}$

Step5: Substitute $x=4$ into equation c)

$A(4) + 5 - 2(4) - 7 = 14$

Step6: Simplify and solve for A

$4A + 5 - 8 - 7 = 14$
$4A - 10 = 14$
$4A = 14 + 10$
$A = \frac{24}{4}$

Answer:

a) $A=7$
b) $A=9$
c) $A=6$