Sure, let's solve the equation step-by-step:
Given equation:
[tex]\[
\sqrt{5x + 56} - 3 = 1
\][/tex]
Step 1: Isolate the square root term.
Add 3 to both sides of the equation:
[tex]\[
\sqrt{5x + 56} = 1 + 3
\][/tex]
Which simplifies to:
[tex]\[
\sqrt{5x + 56} = 4
\][/tex]
Step 2: Remove the square root by squaring both sides.
Square both sides of the equation:
[tex]\[
(\sqrt{5x + 56})^2 = 4^2
\][/tex]
This simplifies to:
[tex]\[
5x + 56 = 16
\][/tex]
Step 3: Solve for [tex]\( x \)[/tex].
First, isolate [tex]\( 5x \)[/tex] by subtracting 56 from both sides:
[tex]\[
5x = 16 - 56
\][/tex]
Which simplifies to:
[tex]\[
5x = -40
\][/tex]
Next, divide both sides by 5 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{-40}{5}
\][/tex]
This gives us:
[tex]\[
x = -8
\][/tex]
So, the value of [tex]\( x \)[/tex] is:
[tex]\[
\boxed{-8}
\][/tex]
