Question

Solve for X 1. - 6x + 14 < =28 OR 9x + 15 <-12

Answer 1

Solution:

1)

$-6x + 14\leq 28$

Solve the inequality for "x"

From given,

$-6x + 14\leq 28$

$\mathrm{Subtract\:}14\mathrm{\:from\:both\:sides}\\\\-6x+14-14\le \:28-14\\\\Simplify\\\\-6x\le \:14\\\\\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}$

When, we multiply or divide both sides of inequality by negative number, then we must flip the inequality sign

$\left(-6x\right)\left(-1\right)\ge \:14\left(-1\right)\\\\\mathrm{Simplify}\\\\6x\ge \:-14\\\\\mathrm{Divide\:both\:sides\:by\:}6\\\\\frac{6x}{6}\ge \frac{-14}{6}\\\\x \geq -2.333$

The solution set is given as:

$-6x+14\le \:28\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\ge \:-\frac{7}{3}\:\\ \:\mathrm{Decimal:}&\:x\ge \:-2.33333\dots \\ \:\mathrm{Interval\:Notation:}&\:[-\frac{7}{3},\:\infty \:)\end{bmatrix}$

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2)

$9x + 15< - 12$

Solve the inequality for "x"

From given,

$9x+15$

The solution set is given as:

$9x+15$