Solve (4/8(x+3)leqx-7)

$$( \frac { 4 } { 8 } ( x + 3 ) \leq x - 7 )$$

Solve for x

$$x\geq 17$$

Solution Steps

Reduce the fraction \frac{4}{8} to lowest terms by extracting and canceling out 4.

$$\frac{1}{2}\left(x+3\right)\leq x-7$$

Use the distributive property to multiply \frac{1}{2} by x+3.

$$\frac{1}{2}x+\frac{1}{2}\times 3\leq x-7$$

Multiply \frac{1}{2} and 3 to get \frac{3}{2}.

$$\frac{1}{2}x+\frac{3}{2}\leq x-7$$

Subtract x from both sides.

$$\frac{1}{2}x+\frac{3}{2}-x\leq -7$$

Combine \frac{1}{2}x and -x to get -\frac{1}{2}x.

$$-\frac{1}{2}x+\frac{3}{2}\leq -7$$

Subtract \frac{3}{2} from both sides.

$$-\frac{1}{2}x\leq -7-\frac{3}{2}$$

Convert -7 to fraction -\frac{14}{2}.

$$-\frac{1}{2}x\leq -\frac{14}{2}-\frac{3}{2}$$

Since -\frac{14}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{2}x\leq \frac{-14-3}{2}$$

Subtract 3 from -14 to get -17.

$$-\frac{1}{2}x\leq -\frac{17}{2}$$

Multiply both sides by -2, the reciprocal of -\frac{1}{2}. Since -\frac{1}{2} is negative, the inequality direction is changed.

$$x\geq -\frac{17}{2}\left(-2\right)$$

Express -\frac{17}{2}\left(-2\right) as a single fraction.

$$x\geq \frac{-17\left(-2\right)}{2}$$

Multiply -17 and -2 to get 34.

$$x\geq \frac{34}{2}$$

Divide 34 by 2 to get 17.

$$x\geq 17$$