Question

Need help with number 3 inequalities with variables on both sides

Answer 1

Answer:

x ≤ 2

Step-by-step explanation:

We are given the inequality:

$\displaystyle{2x-3 \leq \dfrac{x}{2}}$

First, get rid of the denominator by multiplying both sides by 2:

$\displaystyle{2x\cdot 2-3\cdot 2 \leq \dfrac{x}{2}\cdot 2}\\\\\displaystyle{4x-6 \leq x}$

Add both sides by 6 then subtract both sides by x:

$\displaystyle{4x-6+6 \leq x+6}\\\\\displaystyle{4x \leq x+6}\\\\\displaystyle{4x-x \leq x+6-x}\\\\\displaystyle{4x-x \leq 6}\\\\\displaystyle{3x \leq 6}$

Then divide both sides by 3:

$\displaystyle{\dfrac{3x}{3} \leq \dfrac{6}{3}}\\\\\displaystyle{x \leq 2}$

Therefore, the answer is x ≤ 2

Answer 2

Answer: $x \leq 2$

Step-by-step explanation: Given $2x - 3 \leq \frac{x}{2}$, we multiply 2 by both sides to cancel out the 2 in the denominator (multiplying by a number in a fraction turns it into 1, and since the denominator is one, it is the same as saying the number [or variable] on the numerator by itself.)

We then get $4x - 6 \leq x$.

Adding 6 to both sides, we get $4x \leq x + 6$.

Subtracting x from both sides, we get $3x \leq 6$

Dividing by 3 from both sides, we get $x \leq 2$

Hope this helped!