Solve 1/3(x-4)+2leq1/5(x+5)

$$\frac { 1 } { 3 } ( x - 4 ) + 2 \leq \frac { 1 } { 5 } ( x + 5 )$$

Solve for x

$$x\leq \frac{5}{2}$$

Solution Steps

Use the distributive property to multiply \frac{1}{3} by x-4.

$$\frac{1}{3}x+\frac{1}{3}\left(-4\right)+2\leq \frac{1}{5}\left(x+5\right)$$

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

$$\frac{1}{3}x+\frac{-4}{3}+2\leq \frac{1}{5}\left(x+5\right)$$

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

$$\frac{1}{3}x-\frac{4}{3}+2\leq \frac{1}{5}\left(x+5\right)$$

Convert 2 to fraction \frac{6}{3}.

$$\frac{1}{3}x-\frac{4}{3}+\frac{6}{3}\leq \frac{1}{5}\left(x+5\right)$$

Since -\frac{4}{3} and \frac{6}{3} have the same denominator, add them by adding their numerators.

$$\frac{1}{3}x+\frac{-4+6}{3}\leq \frac{1}{5}\left(x+5\right)$$

Add -4 and 6 to get 2.

$$\frac{1}{3}x+\frac{2}{3}\leq \frac{1}{5}\left(x+5\right)$$

Use the distributive property to multiply \frac{1}{5} by x+5.

$$\frac{1}{3}x+\frac{2}{3}\leq \frac{1}{5}x+\frac{1}{5}\times 5$$

Cancel out 5 and 5.

$$\frac{1}{3}x+\frac{2}{3}\leq \frac{1}{5}x+1$$

Subtract \frac{1}{5}x from both sides.

$$\frac{1}{3}x+\frac{2}{3}-\frac{1}{5}x\leq 1$$

Combine \frac{1}{3}x and -\frac{1}{5}x to get \frac{2}{15}x.

$$\frac{2}{15}x+\frac{2}{3}\leq 1$$

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

$$\frac{2}{15}x\leq 1-\frac{2}{3}$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{2}{15}x\leq \frac{3}{3}-\frac{2}{3}$$

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

$$\frac{2}{15}x\leq \frac{3-2}{3}$$

Subtract 2 from 3 to get 1.

$$\frac{2}{15}x\leq \frac{1}{3}$$

Multiply both sides by \frac{15}{2}, the reciprocal of \frac{2}{15}. Since \frac{2}{15} is positive, the inequality direction remains the same.

$$x\leq \frac{1}{3}\times \frac{15}{2}$$

Multiply \frac{1}{3} times \frac{15}{2} by multiplying numerator times numerator and denominator times denominator.

$$x\leq \frac{1\times 15}{3\times 2}$$

Do the multiplications in the fraction \frac{1\times 15}{3\times 2}.

$$x\leq \frac{15}{6}$$

Reduce the fraction \frac{15}{6} to lowest terms by extracting and canceling out 3.

$$x\leq \frac{5}{2}$$