Question

Simplify the inequalities and match them with the graphs that represent them. 7x < 42 3x >15 2x > 12 X + 1 < 8

Answer 1

Part 1

Given the inequality:

`\begin{gathered} 7x<42 \\ \text{Divide both sides by 7} \\ (7x)/(7)<(42)/(7) \\ x<6 \end{gathered}`

The corresponding graph is the 3rd graph.

Part 2

Given the inequality:

`\begin{gathered} 3x>15 \\ \text{Divide both sides by }3 \\ (3x)/(3)>(15)/(3) \\ x>5 \end{gathered}`

The corresponding graph is the 4th graph.

Part 3

Given the inequality:

`\begin{gathered} 2x>12 \\ \text{Divide both sides by }3 \\ (2x)/(2)>(12)/(2) \\ x>6 \end{gathered}`

The corresponding graph is the 1st graph.

Part 4

Given the inequality:

`\begin{gathered} x+1<8 \\ \text{Subtract 1 from both sides} \\ x+1-1<8-1 \\ x<7 \end{gathered}`

The corresponding graph is the 2nd graph.