Question

HELP HOW DO I SOLVE THIS

Answer 1

(a) x ≥ 4

Explanation:

You want to solve the inequality (8x +3)/5 ≥ 7.

Three step solution

You solve this inequality the same way you would solve a 3-step equation. Undo the operations done to the variable.

`(8x+3)/(5)\ge 7\qquad\text{given}\\\\8x+3 \ge 35\qquad\text{multiply by 5}\\\\8x\ge32\qquad\text{subtract 3}\\\\\boxed{x \ge 4}\qquad\text{divide by 8}`

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Additional comment

As you see, the inequality is solved the same way that an equation would be solved. The only difference is that any multiplication or division by a negative number reverses the inequality symbol.

2 ≥ 1

-2 ≤ -1