Solve equations and inequalities in one variable - HiSet: High School Equivalency Test: Math

Card 0 of 2

Question

Solve.

$\frac{x}{4}+11=15$

Answer

In order to solve for the variable, , we need to isolate it on the left side of the equation. We will do this by reversing the operations done to the variable by performing the opposite of each operation on both sides of the equation.

Let's begin by rewriting the given equation.

$\frac{x}{4}+11=15$

Subtract from both sides of the equation.

$\frac{x}{4}+11-11=15-11$

Simplify.

$\frac{x}{4}=4$

Multiply both sides of the equation by .

$\frac{x}{4}\times 4=4\times 4$

Solve.

Compare your answer with the correct one above

Question

Give the solution set of the inequality

$\left | -4x + 13 \right | \ge 9$

Answer

$\left | -4x + 13 \right | \ge 9$ can be rewritten as the compound inequality

$-4x + 13 \le - 9 \textup{ or } -4x + 13 \ge 9$ .

The solution set will be the union of the two individual solution sets. Find the solution set of the first inequality as follows:

Isolate by first subtracting from both sides:

$-4x + 13 \le - 9$

$-4x + 13- 13 \le - 9 - 13$

$-4x \le -22$

Divide both sides by , reversing the direction of the inequality symbol, since you are dividing by a negative number:

$-4x \div (-4){ \color{Red} \ge} -22 \div (-4)$

$x \ge 5\frac{1}{2}$ .

In interval notation, this is the set $\left [ 5 \frac{1}{2} , \infty \right )$ .

Find the solution set of the other inequality similarly:

$-4x + 13 \ge 9$

$-4x + 13 - 13 \ge 9 - 13$

$-4x \ge -4$

$-4x \div (-4) \le -4 \div (-4)$

$x \le 1$

In interval notation, this is the set $\left ( -\infty, 1 \right ]$ .

The union of these sets is the solution set: $\left ( -\infty, 1 \right ] \cup \left [ 5 \frac{1}{2} , \infty \right )$ .

Compare your answer with the correct one above

Tap the card to reveal the answer