Sure, let's solve the given linear equation step-by-step.
Given equation:
[tex]\[ 5x - 2 = 33 \][/tex]
Step 1: To isolate the term involving [tex]\( x \)[/tex], we first need to get rid of the constant on the left side. We do this by adding 2 to both sides of the equation.
[tex]\[ 5x - 2 + 2 = 33 + 2 \][/tex]
This simplifies to:
[tex]\[ 5x = 35 \][/tex]
Step 2: Next, we need to solve for [tex]\( x \)[/tex] by isolating it. We do this by dividing both sides of the equation by 5:
[tex]\[ \frac{5x}{5} = \frac{35}{5} \][/tex]
This simplifies to:
[tex]\[ x = 7 \][/tex]
So, the solution to the equation [tex]\( 5x - 2 = 33 \)[/tex] is:
[tex]\[ x = 7 \][/tex]
Verify: To ensure our solution is correct, we can substitute [tex]\( x = 7 \)[/tex] back into the original equation and check if both sides are equal:
[tex]\[ 5(7) - 2 = 35 - 2 = 33 \][/tex]
Since both sides of the original equation are equal when [tex]\( x = 7 \)[/tex], our solution is confirmed to be correct.
