Solve 3/4(x-7)geqx+2

$$\frac { 3 } { 4 } ( x - 7 ) \geq x + 2$$

Solve for x

$$x\leq -29$$

Solution Steps

Use the distributive property to multiply \frac{3}{4} by x-7.

$$\frac{3}{4}x+\frac{3}{4}\left(-7\right)\geq x+2$$

Express \frac{3}{4}\left(-7\right) as a single fraction.

$$\frac{3}{4}x+\frac{3\left(-7\right)}{4}\geq x+2$$

Multiply 3 and -7 to get -21.

$$\frac{3}{4}x+\frac{-21}{4}\geq x+2$$

Fraction \frac{-21}{4} can be rewritten as -\frac{21}{4} by extracting the negative sign.

$$\frac{3}{4}x-\frac{21}{4}\geq x+2$$

Subtract x from both sides.

$$\frac{3}{4}x-\frac{21}{4}-x\geq 2$$

Combine \frac{3}{4}x and -x to get -\frac{1}{4}x.

$$-\frac{1}{4}x-\frac{21}{4}\geq 2$$

Add \frac{21}{4} to both sides.

$$-\frac{1}{4}x\geq 2+\frac{21}{4}$$

Convert 2 to fraction \frac{8}{4}.

$$-\frac{1}{4}x\geq \frac{8}{4}+\frac{21}{4}$$

Since \frac{8}{4} and \frac{21}{4} have the same denominator, add them by adding their numerators.

$$-\frac{1}{4}x\geq \frac{8+21}{4}$$

Add 8 and 21 to get 29.

$$-\frac{1}{4}x\geq \frac{29}{4}$$

Multiply both sides by -4, the reciprocal of -\frac{1}{4}. Since -\frac{1}{4} is negative, the inequality direction is changed.

$$x\leq \frac{29}{4}\left(-4\right)$$

Express \frac{29}{4}\left(-4\right) as a single fraction.

$$x\leq \frac{29\left(-4\right)}{4}$$

Multiply 29 and -4 to get -116.

$$x\leq \frac{-116}{4}$$

Divide -116 by 4 to get -29.

$$x\leq -29$$