To solve the inequality [tex]\( 5 - 8x < 2x + 3 \)[/tex], let's break down the steps required in detail.
### Step-by-Step Solution:
Step 1: Subtract 3 from both sides of the inequality.
This helps in simplifying the constant terms on each side.
[tex]\[ 5 - 8x - 3 < 2x + 3 - 3 \][/tex]
Simplify the constants:
[tex]\[ 2 - 8x < 2x \][/tex]
Step 2: Subtract 2x from both sides of the inequality.
This step isolates the variable [tex]\( x \)[/tex] on one side.
[tex]\[ 2 - 8x - 2x < 2x - 2x \][/tex]
Combine like terms:
[tex]\[ 2 - 10x < 0 \][/tex]
Step 3: Divide both sides of the inequality by the coefficient of [tex]\( x \)[/tex] (which is -10).
When dividing by a negative number, remember to reverse the inequality sign.
[tex]\[ -10x < -2 \][/tex]
Divide both sides by -10:
[tex]\[ x > \frac{-2}{-10} \][/tex]
Simplify the fraction:
[tex]\[ x > \frac{1}{5} \][/tex]
The missing step in solving the inequality is "Subtract 2x from both sides of the inequality."
