Solve and graph this inequality:
`\frac{1}{4}x+3>-10`
You will need to move your point below to earn full credit. 👇
To solve the inequality, we need to isolate the variable x.
First, we can subtract 3 from both sides of the inequality:
\(\frac{1}{4}x+3-3>-10-3\)
Simplifying, we have:
\(\frac{1}{4}x>-13\)
To eliminate the fraction, we can multiply both sides of the inequality by 4:
\(4\left(\frac{1}{4}x\right)>4(-13)\)
Simplifying, we have:
\(x>-52\)
Now, let's graph the solution on a number line.
We represent the solution graph as a shaded region starting from -52 and extending towards positive infinity. We use an open circle to indicate that -52 itself is not included in the solution:
-52 -51 -50 -49 ... 0 1 2 3 ...
----------------------------------------->
(====================>
x > -52