Question

lesson 13 practice problems
1 for each inequality, find two values for $x$ that make the inequality true and two values that make it false.
a. $x + 3 > 70$
b. $x + 3 < 70$
c. $-5x < 2$
d. $5x < 2$

Explanation:

Step1: Solve for true values (a)

Rearrange inequality: $x > 70 - 3$ → $x > 67$. Pick $x=68, x=69$.

Step2: Solve for false values (a)

Values where $x \leq 67$. Pick $x=67, x=0$.

Step3: Solve for true values (b)

Rearrange inequality: $x < 70 - 3$ → $x < 67$. Pick $x=66, x=0$.

Step4: Solve for false values (b)

Values where $x \geq 67$. Pick $x=67, x=70$.

Step5: Solve for true values (c)

Rearrange inequality: $x > \frac{2}{-5}$ → $x > -0.4$. Pick $x=0, x=1$.

Step6: Solve for false values (c)

Values where $x \leq -0.4$. Pick $x=-1, x=-2$.

Step7: Solve for true values (d)

Rearrange inequality: $x < \frac{2}{5}$ → $x < 0.4$. Pick $x=0, x=-1$.

Step8: Solve for false values (d)

Values where $x \geq 0.4$. Pick $x=1, x=2$.

Answer:

a. True values: $x=68$, $x=69$; False values: $x=67$, $x=0$
b. True values: $x=66$, $x=0$; False values: $x=67$, $x=70$
c. True values: $x=0$, $x=1$; False values: $x=-1$, $x=-2$
d. True values: $x=0$, $x=-1$; False values: $x=1$, $x=2$