To find the value of [tex]\( x \)[/tex] in the equation [tex]\( 5(3x + 4) = 23 \)[/tex], follow these steps:
1. Expand the left-hand side:
[tex]\[ 5(3x + 4) = 23 \][/tex]
Multiply out the terms inside the parentheses:
[tex]\[ 5 \cdot 3x + 5 \cdot 4 = 23 \][/tex]
Simplifying that, we get:
[tex]\[ 15x + 20 = 23 \][/tex]
2. Isolate the term with [tex]\( x \)[/tex] on one side:
Subtract 20 from both sides to get:
[tex]\[ 15x + 20 - 20 = 23 - 20 \][/tex]
Simplifying that, we obtain:
[tex]\[ 15x = 3 \][/tex]
3. Solve for [tex]\( x \)[/tex]:
To isolate [tex]\( x \)[/tex], divide both sides by 15:
[tex]\[ x = \frac{3}{15} \][/tex]
Simplify the fraction:
[tex]\[ x = \frac{1}{5} \][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\(\frac{1}{5}\)[/tex], or equivalently,
[tex]\[ x = 0.2 \][/tex]
Looking at the given choices, the answer that corresponds to this is:
[tex]$\frac{2}{5}$[/tex]
