Answer :
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]
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]
