Question

ear equations and inequalities
sara wants to find the input value that produces the same output for the functions represented by the tables
$f(x)=-0.5x + 2$

$x$	$f(x)$
-2	3
-1	2.5
0	2
1	1.5
2	1
3	0.5

$g(x)=2x - 3$

$x$	$g(x)$
-2
-1
0
1
2
3

what is the input value that produces the same output value in both charts?
-1
2
1
-2

Explanation:

Step1: Set functions equal

Set $f(x) = g(x)$:
$$-0.5x + 2 = 2x - 3$$

Step2: Isolate x terms

Add $0.5x$ to both sides:
$$2 = 2.5x - 3$$

Step3: Isolate constant terms

Add 3 to both sides:
$$5 = 2.5x$$

Step4: Solve for x

Divide by 2.5:
$$x = \frac{5}{2.5} = 2$$

Step5: Verify with tables

For $x=2$, $f(2)=-0.5(2)+2=1$, $g(2)=2(2)-3=1$. Outputs match.

Answer:

2