Question

graphing the solution of an inequality on the number line
graph the solution of this inequality:
$\frac{3}{4}(x + 8)>\frac{1}{2}(2x + 10)$

drag a point to the number line.
show example

Explanation:

Step1: Expand both sides

First, expand $\frac{3}{4}(x + 8)$ and $\frac{1}{2}(2x+10)$.
$\frac{3}{4}(x + 8)=\frac{3}{4}x+6$ and $\frac{1}{2}(2x + 10)=x + 5$.
So the inequality becomes $\frac{3}{4}x+6>x + 5$.

Step2: Move terms with x to one - side

Subtract $\frac{3}{4}x$ from both sides:
$6>x-\frac{3}{4}x + 5$.
Simplify the right - hand side: $x-\frac{3}{4}x=\frac{1}{4}x$, so $6>\frac{1}{4}x + 5$.
Then subtract 5 from both sides: $6 - 5>\frac{1}{4}x$, which gives $1>\frac{1}{4}x$.

Step3: Solve for x

Multiply both sides by 4 to isolate x: $4>x$, or $x < 4$.

Answer:

On the number line, we use an open circle at 4 (because the inequality is $x<4$, not $x\leqslant4$) and draw an arrow to the left.