Question

question
what is the solution to this equation?
$4(5x + 3) = 14x + 30$
a. $x = -7$
b. $x = -3$
c. $x = 3$
d. $x = 7$

Explanation:

Step1: Expand the left side

Using the distributive property \(a(b + c)=ab+ac\), we expand \(4(5x + 3)\) to get \(4\times5x+4\times3 = 20x+12\). So the equation becomes \(20x + 12=14x + 30\).

Step2: Subtract \(14x\) from both sides

Subtracting \(14x\) from both sides gives \(20x-14x + 12=14x-14x + 30\), which simplifies to \(6x+12 = 30\).

Step3: Subtract 12 from both sides

Subtracting 12 from both sides: \(6x+12 - 12=30 - 12\), so \(6x=18\).

Step4: Divide both sides by 6

Dividing both sides by 6: \(\frac{6x}{6}=\frac{18}{6}\), which gives \(x = 3\).

Answer:

C. \(x = 3\)