# choose the correct solution and graph for the inequality.

z + 1/8 > 1/5

choose the correct solution and graph for the inequality.

y + 7 <_ 5

## z + 1/8 > 1/5

z > 1/5 - 1/8
z < 3/40
you should see that in your choices

y + 7 ≤ 5
y ≤ 5-7
y ≤ -2

## For the inequality z + 1/8 > 1/5:

Solution: z > 1/5 - 1/8

Graph:

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-1/5 0 1/5 1/4 1/3

For the inequality y + 7 ≤ 5:

Solution: y ≤ 5 - 7

Graph:

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-7 -6 -5 -4 -3

## To solve the inequality z + 1/8 > 1/5, we will subtract 1/8 from both sides of the inequality:

z + 1/8 - 1/8 > 1/5 - 1/8

This simplifies to:

z > 8/40 - 5/40
z > 3/40

So, the solution to the inequality z + 1/8 > 1/5 is z > 3/40.

To graph this inequality, we will represent it on a number line. Since z is greater than 3/40, we will represent it with an open circle at 3/40 and shade the line to the right, indicating all values greater than 3/40 are solutions to the inequality. The graph will look like:

--------●======================>

Where the open circle represents 3/40 and the line extending to the right indicates all values greater than 3/40.

Now moving to the second inequality, y + 7 ≤ 5.

To solve this inequality, we will subtract 7 from both sides of the inequality:

y + 7 - 7 ≤ 5 - 7

This simplifies to:

y ≤ -2

So, the solution to the inequality y + 7 ≤ 5 is y ≤ -2.

To graph this inequality, we will represent it on a number line. Since y is less than or equal to -2, we will represent it with a closed circle at -2 and shade the line to the left, indicating all values less than or equal to -2 are solutions to the inequality. The graph will look like:

<========●----------------

Where the closed circle represents -2 and the line extending to the left indicates all values less than or equal to -2.

## To solve inequalities and graph the solutions, we need to follow a few steps:

For the inequality z + 1/8 > 1/5:

Step 1: Subtract 1/8 from both sides of the inequality to isolate the variable.

z + 1/8 - 1/8 > 1/5 - 1/8

z > 8/40 - 5/40

z > 3/40

Step 2: Simplify the result.

Step 3: Graph the solution on a number line. Since the inequality is "greater than," the graph will be an open circle at 3/40 and a shaded region to the right.

________o__________________>

The correct solution is z > 3/40.

For the inequality y + 7 ≤ 5:

Step 1: Subtract 7 from both sides of the inequality.

y + 7 - 7 ≤ 5 - 7

y ≤ -2

Step 2: Simplify the result.

Step 3: Graph the solution on a number line. Since the inequality is "less than or equal to," the graph will be a closed circle at -2 and a shaded region to the left.

<_________o___________________

The correct solution is y ≤ -2.