Question

solve the following and graph the solutions: -2x + 7 < 5 and -2x + 7 > - 5 x > 1 and x < 6 x > 1 and x < 6 x > 1 and x < 6 x > 1 and x < 6 x > 1 and x < 6

Explanation:

Step1: Solve first inequality

$-2x + 7 < 5$
Subtract 7: $-2x < -2$
Divide by -2 (reverse sign): $x > 1$

Step2: Solve second inequality

$-2x + 7 > -5$
Subtract 7: $-2x > -12$
Divide by -2 (reverse sign): $x < 6$

Step3: Combine solutions

$1 < x < 6$ (open interval, open circles at 1 and 6, shaded between)

Answer:

The correct graph is the one with open circles at 1 and 6, and a line segment connecting them (representing $1 < x < 6$).