Solve 3(2-x)+5 > x-2(x-2) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$3(2-x)+5 > x-2(x-2)$$

Solve for x

$x<\frac{7}{2}$

Solution Steps

Use the distributive property to multiply $3$ by $2-x$.

$$6-3x+5>x-2\left(x-2\right)$$

Add $6$ and $5$ to get $11$.

$$11-3x>x-2\left(x-2\right)$$

Use the distributive property to multiply $-2$ by $x-2$.

$$11-3x>x-2x+4$$

Combine $x$ and $-2x$ to get $-x$.

$$11-3x>-x+4$$

Add $x$ to both sides.

$$11-3x+x>4$$

Combine $-3x$ and $x$ to get $-2x$.

$$11-2x>4$$

Subtract $11$ from both sides.

$$-2x>4-11$$

Subtract $11$ from $4$ to get $-7$.

$$-2x>-7$$

Divide both sides by $-2$. Since $-2$ is negative, the inequality direction is changed.

$$x<\frac{-7}{-2}$$

Fraction $\frac{-7}{-2}$ can be simplified to $\frac{7}{2}$ by removing the negative sign from both the numerator and the denominator.

$$x<\frac{7}{2}$$