Question

for numbers 3a – 3c, circle true or false for each statement based on the following equation.
( y = 40 - 2.5x )
3a. if ( y = 10 ), then ( x = 12 ) \ttrue \tfalse
3b. if ( x = 6 ), then ( y = 26 ) \ttrue \tfalse
3c. if ( y = -5 ), then ( x = 15 ) \ttrue \tfalse

Explanation:

3a

Step1: Substitute \( y = 10 \) into the equation

We have the equation \( y = 40 - 2.5x \). Substitute \( y = 10 \) into it: \( 10 = 40 - 2.5x \)

Step2: Solve for \( x \)

First, rearrange the equation: \( 2.5x = 40 - 10 \)
Simplify the right - hand side: \( 2.5x = 30 \)
Then, divide both sides by \( 2.5 \): \( x=\frac{30}{2.5}=12 \)

Step1: Substitute \( x = 6 \) into the equation

Given \( y = 40 - 2.5x \), substitute \( x = 6 \): \( y=40 - 2.5\times6 \)

Step2: Calculate the value of \( y \)

First, calculate \( 2.5\times6 = 15 \)
Then, \( y = 40-15=25
eq26 \)

Step1: Substitute \( y=-5 \) into the equation

Substitute \( y = - 5 \) into \( y = 40 - 2.5x \): \( - 5=40 - 2.5x \)

Step2: Solve for \( x \)

Rearrange the equation: \( 2.5x=40 + 5 \)
Simplify the right - hand side: \( 2.5x = 45 \)
Divide both sides by \( 2.5 \): \( x=\frac{45}{2.5}=18
eq15 \)

Answer:

TRUE

3b