What is the solution to this equation?

[tex]\[ 4(5x + 3) = 14x + 30 \][/tex]

A. [tex]\( x = 7 \)[/tex]
B. [tex]\( x = -3 \)[/tex]
C. [tex]\( x = -7 \)[/tex]
D. [tex]\( x = 3 \)[/tex]



Answer :

To solve the equation [tex]\(4(5x + 3) = 14x + 30\)[/tex], let's follow a step-by-step approach:

1. Expand the left side of the equation:

[tex]\(4(5x + 3)\)[/tex]

Distribute the [tex]\(4\)[/tex] across the terms inside the parentheses:

[tex]\(20x + 12\)[/tex]

Now the equation looks like:

[tex]\(20x + 12 = 14x + 30\)[/tex]

2. Move all the [tex]\(x\)[/tex] terms to one side:

To do this, subtract [tex]\(14x\)[/tex] from both sides of the equation:

[tex]\(20x + 12 - 14x = 14x + 30 - 14x\)[/tex]

This simplifies to:

[tex]\(6x + 12 = 30\)[/tex]

3. Move the constant terms to the other side:

To isolate the [tex]\(x\)[/tex] term, subtract [tex]\(12\)[/tex] from both sides:

[tex]\(6x + 12 - 12 = 30 - 12\)[/tex]

This simplifies to:

[tex]\(6x = 18\)[/tex]

4. Solve for [tex]\(x\)[/tex]:

Divide both sides by [tex]\(6\)[/tex]:

[tex]\[ x = \frac{18}{6} \][/tex]

Simplifying the fraction we get:

[tex]\(x = 3\)[/tex]

So, the solution to the equation [tex]\(4(5x + 3) = 14x + 30\)[/tex] is [tex]\(x = 3\)[/tex].

Therefore, the correct answer is:

D. [tex]\(x = 3\)[/tex]