Answer :
We want to solve the equation
[tex]$$11x + 15 = 3x - 7.$$[/tex]
Step 1: Isolate the [tex]\( x \)[/tex]-terms by subtracting [tex]\( 3x \)[/tex] from both sides:
[tex]$$
11x + 15 - 3x = 3x - 7 - 3x,
$$[/tex]
which simplifies to:
[tex]$$
8x + 15 = -7.
$$[/tex]
Step 2: Next, remove the constant [tex]\( 15 \)[/tex] from the left-hand side by subtracting [tex]\( 15 \)[/tex] from both sides:
[tex]$$
8x + 15 - 15 = -7 - 15,
$$[/tex]
which gives:
[tex]$$
8x = -22.
$$[/tex]
Step 3: Now, solve for [tex]\( x \)[/tex] by dividing both sides by [tex]\( 8 \)[/tex]:
[tex]$$
x = \frac{-22}{8}.
$$[/tex]
This fraction can be simplified by dividing the numerator and denominator by [tex]\( 2 \)[/tex]:
[tex]$$
x = \frac{-11}{4}.
$$[/tex]
Hence, the solution to the equation is
[tex]$$
\boxed{\frac{-11}{4}} \quad \text{or} \quad -2.75.
$$[/tex]
[tex]$$11x + 15 = 3x - 7.$$[/tex]
Step 1: Isolate the [tex]\( x \)[/tex]-terms by subtracting [tex]\( 3x \)[/tex] from both sides:
[tex]$$
11x + 15 - 3x = 3x - 7 - 3x,
$$[/tex]
which simplifies to:
[tex]$$
8x + 15 = -7.
$$[/tex]
Step 2: Next, remove the constant [tex]\( 15 \)[/tex] from the left-hand side by subtracting [tex]\( 15 \)[/tex] from both sides:
[tex]$$
8x + 15 - 15 = -7 - 15,
$$[/tex]
which gives:
[tex]$$
8x = -22.
$$[/tex]
Step 3: Now, solve for [tex]\( x \)[/tex] by dividing both sides by [tex]\( 8 \)[/tex]:
[tex]$$
x = \frac{-22}{8}.
$$[/tex]
This fraction can be simplified by dividing the numerator and denominator by [tex]\( 2 \)[/tex]:
[tex]$$
x = \frac{-11}{4}.
$$[/tex]
Hence, the solution to the equation is
[tex]$$
\boxed{\frac{-11}{4}} \quad \text{or} \quad -2.75.
$$[/tex]
