Question

Solve each inequality. (Lessons 1-5 and 1-6)

62. $-\mathbf{4}\mathbf{x}+\mathbf{7}\le \mathbf{31}$

Short answer

The solution of the given inequality is $x\ge -6$.

Step-by-step solution

– State the concept

Solving an inequality means modifying the inequality so that the variable is isolated. It is essentially finding the range of values of the variable for which the given inequality is satisfied.

Dividing or multiplying the terms of an inequality by a negative number changes the inequality to its opposite one.

– List the given data

The given inequality is $-4x+7\le 31$.

– Solve the inequality

$-4x+7\le 31$ (Given inequality)

$-4x+7-7\le 31-7$ (Subtract 7 from both sides of the inequality)

$-4x\le 24$ (Simplify)

$\frac{-4x}{-4}\ge \frac{24}{-4}$ (Divide both sides of the inequality by -4)

$x\ge -6$ (Simplify)

So, the solution of the given inequality is $x\ge -6$.