Question

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 ) true
false
b. ( x + 3 < 70 ) true
false
c. ( -5x < 2 ) true
false
d. ( 5x < 2 ) true
false

Explanation:

a. $x + 3 > 70$

Step1: Solve for valid $x$

$x > 70 - 3 \implies x > 67$

Step2: Pick true values

Choose $x=68, x=70$ (both >67)

Step3: Pick false values

Choose $x=67, x=60$ (≤67)

b. $x + 3 < 70$

Step1: Solve for valid $x$

$x < 70 - 3 \implies x < 67$

Step2: Pick true values

Choose $x=66, x=60$ (both <67)

Step3: Pick false values

Choose $x=67, x=70$ (≥67)

c. $-5x < 2$

Step1: Solve for valid $x$

Divide by -5 (reverse inequality): $x > -\frac{2}{5} = -0.4$

Step2: Pick true values

Choose $x=0, x=1$ (both >-0.4)

Step3: Pick false values

Choose $x=-1, x=-0.5$ (≤-0.4)

d. $5x < 2$

Step1: Solve for valid $x$

$x < \frac{2}{5} = 0.4$

Step2: Pick true values

Choose $x=0, x=-1$ (both <0.4)

Step3: Pick false values

Choose $x=1, x=0.5$ (≥0.4)

Answer:

a. True: $x=68$, $x=70$; False: $x=67$, $x=60$
b. True: $x=66$, $x=60$; False: $x=67$, $x=70$
c. True: $x=0$, $x=1$; False: $x=-1$, $x=-0.5$
d. True: $x=0$, $x=-1$; False: $x=1$, $x=0.5$