Sure, let's solve for \(\( x \)\) step-by-step. We are given two expressions:
1. \(\( 15x - 5 \)\)
2. \(\( 13x + 9 \)\)
We need to find the value of \(\( x \)\) that satisfies the equation when these two expressions are equal to each other:
\(\[ 15x - 5 = 13x + 9 \]\)
Step 1: Set up the equation
\(\[ 15x - 5 = 13x + 9 \]\)
Step 2: Get all terms involving \(\( x \)\) on one side and constant terms on the other side
Subtract \(\( 13x \)\) from both sides:
\(\[ 15x - 13x - 5 = 9 \]\)
This simplifies to:
\(\[ 2x - 5 = 9 \]\)
Step 3: Isolate the variable term
Add 5 to both sides to move the constant term to the other side of the equation:
\(\[ 2x - 5 + 5 = 9 + 5 \]\)
Simplify:
\(\[ 2x = 14 \]\)
Step 4: Solve for \(\( x \)\)
Divide both sides by 2 to isolate \(\( x \)\):
\(\[ \frac{2x}{2} = \frac{14}{2} \]\)
This gives:
\(\[ x = 7 \]\)
So, the value of \(\( x \)\) that satisfies the equation is:
\(\[ x = 7 \]\)
Verification:
We can verify this solution by substituting \(\( x = 7 \)\) back into the original expressions to ensure they are equal:
For \(\( 15x - 5 \)\):
\(\[ 15(7) - 5 = 105 - 5 = 100 \]\)
For \(\( 13x + 9 \)\):
\(\[ 13(7) + 9 = 91 + 9 = 100 \]\)
Since both sides are equal when \(\( x = 7 \)\), our solution is correct. Therefore, \(\( x = 7 \)\) is indeed the solution.
