Question
Step 1: Solve and graph this inequality:
`\frac{1}{4}x+3>-10`
`\frac{1}{4}x+3>-10`
Answers
GPT-4o mini
To solve the inequality \(\frac{1}{4}x + 3 > -10\), follow these steps:
### Step 1: Isolate the variable \(x\)
1. Start by subtracting \(3\) from both sides of the inequality:
\[
\frac{1}{4}x + 3 - 3 > -10 - 3
\]
\[
\frac{1}{4}x > -13
\]
2. Next, to eliminate the fraction, multiply both sides by \(4\) (since \(4\) is positive, the inequality sign remains the same):
\[
4 \cdot \frac{1}{4}x > 4 \cdot -13
\]
\[
x > -52
\]
### Step 2: Graph the solution
To graph the inequality \(x > -52\):
1. Draw a number line.
2. Locate \(-52\) on the number line.
3. Since the inequality is strict (greater than, not greater than or equal to), draw an open circle at \(-52\), indicating that \(-52\) is not included in the solution.
4. Shade the line to the right of \(-52\) to indicate all numbers greater than \(-52\).
### Summary of the solution
The solution to the inequality \(\frac{1}{4}x + 3 > -10\) is:
\[
x > -52
\]
And its graph consists of a number line with an open circle at \(-52\) and shading to the right.
### Step 1: Isolate the variable \(x\)
1. Start by subtracting \(3\) from both sides of the inequality:
\[
\frac{1}{4}x + 3 - 3 > -10 - 3
\]
\[
\frac{1}{4}x > -13
\]
2. Next, to eliminate the fraction, multiply both sides by \(4\) (since \(4\) is positive, the inequality sign remains the same):
\[
4 \cdot \frac{1}{4}x > 4 \cdot -13
\]
\[
x > -52
\]
### Step 2: Graph the solution
To graph the inequality \(x > -52\):
1. Draw a number line.
2. Locate \(-52\) on the number line.
3. Since the inequality is strict (greater than, not greater than or equal to), draw an open circle at \(-52\), indicating that \(-52\) is not included in the solution.
4. Shade the line to the right of \(-52\) to indicate all numbers greater than \(-52\).
### Summary of the solution
The solution to the inequality \(\frac{1}{4}x + 3 > -10\) is:
\[
x > -52
\]
And its graph consists of a number line with an open circle at \(-52\) and shading to the right.