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