Question

5 solve the inequality 7 - 2x > -13; 6 solve the inequality 2 - 6x < 20

Explanation:

Solving Inequality 5: \( 7 - 2x > -13 \)

Step1: Subtract 7 from both sides

To isolate the term with \( x \), we subtract 7 from both sides of the inequality.
\( 7 - 2x - 7 > -13 - 7 \)
Simplifying both sides, we get:
\( -2x > -20 \)

Step2: Divide by -2 and reverse inequality

When dividing an inequality by a negative number, the direction of the inequality sign reverses. We divide both sides by -2.
\( \frac{-2x}{-2} < \frac{-20}{-2} \)
Simplifying, we obtain:
\( x < 10 \)

Step1: Subtract 2 from both sides

To isolate the term with \( x \), we subtract 2 from both sides of the inequality.
\( 2 - 6x - 2 < 20 - 2 \)
Simplifying both sides, we get:
\( -6x < 18 \)

Step2: Divide by -6 and reverse inequality

When dividing an inequality by a negative number, the direction of the inequality sign reverses. We divide both sides by -6.
\( \frac{-6x}{-6} > \frac{18}{-6} \)
Simplifying, we obtain:
\( x > -3 \)

Answer:

\( x < 10 \)

Solving Inequality 6: \( 2 - 6x < 20 \)