Solve -2x+7 >= (x)/(7)-3 | 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

$$-2x+7 \geq \frac{ x }{ 7 } -3$$

Solve for x

$x\leq \frac{14}{3}$

Solution Steps

Multiply both sides of the equation by $7$. Since $7$ is positive, the inequality direction remains the same.

$$-14x+49\geq x-21$$

Subtract $x$ from both sides.

$$-14x+49-x\geq -21$$

Combine $-14x$ and $-x$ to get $-15x$.

$$-15x+49\geq -21$$

Subtract $49$ from both sides.

$$-15x\geq -21-49$$

Subtract $49$ from $-21$ to get $-70$.

$$-15x\geq -70$$

Divide both sides by $-15$. Since $-15$ is negative, the inequality direction is changed.

$$x\leq \frac{-70}{-15}$$

Reduce the fraction $\frac{-70}{-15}$ to lowest terms by extracting and canceling out $-5$.

$$x\leq \frac{14}{3}$$