Solve 5/2x+15/2-4leq-4x+12+6

$$\frac{ 5 }{ 2 } x+ \frac{ 15 }{ 2 } -4 \leq -4x+12+6$$

Solve for x

$$x\leq \frac{29}{13}$$

Solution Steps

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

$$\frac{5}{2}x+\frac{15}{2}-\frac{8}{2}\leq -4x+12+6$$

Since \frac{15}{2} and \frac{8}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{2}x+\frac{15-8}{2}\leq -4x+12+6$$

Subtract 8 from 15 to get 7.

$$\frac{5}{2}x+\frac{7}{2}\leq -4x+12+6$$

Add 12 and 6 to get 18.

$$\frac{5}{2}x+\frac{7}{2}\leq -4x+18$$

Add 4x to both sides.

$$\frac{5}{2}x+\frac{7}{2}+4x\leq 18$$

Combine \frac{5}{2}x and 4x to get \frac{13}{2}x.

$$\frac{13}{2}x+\frac{7}{2}\leq 18$$

Subtract \frac{7}{2} from both sides.

$$\frac{13}{2}x\leq 18-\frac{7}{2}$$

Convert 18 to fraction \frac{36}{2}.

$$\frac{13}{2}x\leq \frac{36}{2}-\frac{7}{2}$$

Since \frac{36}{2} and \frac{7}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13}{2}x\leq \frac{36-7}{2}$$

Subtract 7 from 36 to get 29.

$$\frac{13}{2}x\leq \frac{29}{2}$$

Multiply both sides by \frac{2}{13}, the reciprocal of \frac{13}{2}. Since \frac{13}{2} is positive, the inequality direction remains the same.

$$x\leq \frac{29}{2}\times \frac{2}{13}$$

Multiply \frac{29}{2} times \frac{2}{13} by multiplying numerator times numerator and denominator times denominator.

$$x\leq \frac{29\times 2}{2\times 13}$$

Cancel out 2 in both numerator and denominator.

$$x\leq \frac{29}{13}$$