Solve 5x/9<8

Question

. Write the improper fraction in your answer as a mixed number. Make sure to write your inequality so that x
comes first.

Answer 1

To solve the inequality \( \frac{5x}{9} < 8 \), we will isolate \( x \).

1. Multiply both sides of the inequality by \( 9 \) to get rid of the fraction: \[ 5x < 8 \times 9 \] \[ 5x < 72 \]

2. Now, divide both sides by \( 5 \) to solve for \( x \): \[ x < \frac{72}{5} \]

3. Next, we convert \( \frac{72}{5} \) into a mixed number. To do this, divide \( 72 \) by \( 5 \): \[ 72 \div 5 = 14 \quad \text{remainder } 2 \] This means that: \[ \frac{72}{5} = 14 \frac{2}{5} \]

Putting it all together, we can write the inequality as: \[ x < 14 \frac{2}{5} \]

So the final answer is: \[ x < 14 \frac{2}{5} \]

Answer 2

Solve 7.9x≤0
. Make sure to write your inequality so that x
comes first.

Answer 3

To solve the inequality \(7.9x \leq 0\), we will isolate \(x\).

1. Divide both sides of the inequality by \(7.9\): \[ x \leq \frac{0}{7.9} \]

2. Simplifying gives: \[ x \leq 0 \]

Now, we can write the inequality so that \(x\) comes first: \[ x \leq 0 \]

So the final answer is: \[ x \leq 0 \]

Answer 4

Use the image to answer the question.

A number line ranges from negative 10 to 10 with numbers listed in unit increments. An open point is plotted on the number line at 0.25. A leftward arrow is marked on the number line that originates at the open circle and goes beyond negative 10. A tick mark is placed at 0.25.

What linear inequality is shown graphed on the number line? Make sure to write your inequality so that x
comes first.

Note: You will find the option to add a >
, <
, ≥
, or ≤
symbol in the Comparison (<)
keyboard.

(1 point)

Answer 5

Based on the description of the number line:

• There is an open point at \(0.25\), which means that \(0.25\) is not included in the solution.
• There is a leftward arrow originating from \(0.25\), indicating that the values of \(x\) are less than \(0.25\) and extend indefinitely to the left.

Thus, we can express this situation as a linear inequality where \(x\) is less than \(0.25\):

\[ x < 0.25 \]

So the final answer for the inequality, with \(x\) coming first, is: \[ x < 0.25 \]