Sure, let’s solve the equation step-by-step:
We start with:
[tex]\[ 17x - 9 = 10x + 12 \][/tex]
Step 1: Move all terms involving [tex]\( x \)[/tex] to one side of the equation.
Subtract [tex]\( 10x \)[/tex] from both sides to isolate the [tex]\( x \)[/tex] terms:
[tex]\[ 17x - 10x - 9 = 12 \][/tex]
Step 2: Combine like terms.
Simplify the expression by combining the [tex]\( x \)[/tex] terms:
[tex]\[ 7x - 9 = 12 \][/tex]
Step 3: Move all constant terms to the other side of the equation.
Add 9 to both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[ 7x - 9 + 9 = 12 + 9 \][/tex]
Simplifying the constants on both sides, we get:
[tex]\[ 7x = 21 \][/tex]
Step 4: Solve for [tex]\( x \)[/tex].
Divide both sides of the equation by 7 to isolate [tex]\( x \)[/tex]:
[tex]\[ x = \frac{21}{7} \][/tex]
Simplifying the fraction:
[tex]\[ x = 3 \][/tex]
So, the solution to the equation [tex]\( 17x - 9 = 10x + 12 \)[/tex] is:
[tex]\[ x = 3 \][/tex]
