Question

exit ticket
solve each inequality. graph the solution on a number line.

1. $3a \

eq 9$

1. $-5 + x \leq 4$
2. $y - 4 \leq 2$
3. $-2z > 4.2$
4. $\frac{b}{2} \geq \frac{1}{4}$

Explanation:

Step1: Isolate $a$

Divide both sides by 3:
$\frac{3a}{3}
eq \frac{9}{3}$

Step2: Simplify for $a$

$a
eq 3$

Step1: Isolate $x$

Add 5 to both sides:
$-5 + x + 5 \leq 4 + 5$

Step2: Simplify for $x$

$x \leq 9$

Step1: Isolate $y$

Add 4 to both sides:
$y - 4 + 4 \leq 2 + 4$

Step2: Simplify for $y$

$y \leq 6$

Step1: Isolate $z$

Divide by -2, reverse inequality:
$\frac{-2z}{-2} < \frac{4.2}{-2}$

Step2: Simplify for $z$

$z < -2.1$

Step1: Isolate $b$

Multiply by 2:
$\frac{b}{2} \times 2 \geq \frac{1}{4} \times 2$

Step2: Simplify for $b$

$b \geq \frac{1}{2}$

Answer:

1. $a

eq 3$
(Number line: Open circle at 3, shade all regions left and right of 3)

1. $x \leq 9$

(Number line: Closed circle at 9, shade all regions left of 9)

1. $y \leq 6$

(Number line: Closed circle at 6, shade all regions left of 6)

1. $z < -2.1$

(Number line: Open circle at -2.1, shade all regions left of -2.1)

1. $b \geq \frac{1}{2}$

(Number line: Closed circle at $\frac{1}{2}$, shade all regions right of $\frac{1}{2}$)