Solve 5-2/5(x+24)=-3/4(15+x)

$$5- \frac{ 2 }{ 5 } (x+24)=- \frac{ 3 }{ 4 } (15+x)$$

Solve for x

$$x=-19$$

Steps for Solving Linear Equation

Use the distributive property to multiply -\frac{2}{5} by x+24.

$$5-\frac{2}{5}x-\frac{2}{5}\times 24=-\frac{3}{4}\left(15+x\right)$$

Express -\frac{2}{5}\times 24 as a single fraction.

$$5-\frac{2}{5}x+\frac{-2\times 24}{5}=-\frac{3}{4}\left(15+x\right)$$

Multiply -2 and 24 to get -48.

$$5-\frac{2}{5}x+\frac{-48}{5}=-\frac{3}{4}\left(15+x\right)$$

Fraction \frac{-48}{5} can be rewritten as -\frac{48}{5} by extracting the negative sign.

$$5-\frac{2}{5}x-\frac{48}{5}=-\frac{3}{4}\left(15+x\right)$$

Convert 5 to fraction \frac{25}{5}.

$$\frac{25}{5}-\frac{2}{5}x-\frac{48}{5}=-\frac{3}{4}\left(15+x\right)$$

Since \frac{25}{5} and \frac{48}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25-48}{5}-\frac{2}{5}x=-\frac{3}{4}\left(15+x\right)$$

Subtract 48 from 25 to get -23.

$$-\frac{23}{5}-\frac{2}{5}x=-\frac{3}{4}\left(15+x\right)$$

Use the distributive property to multiply -\frac{3}{4} by 15+x.

$$-\frac{23}{5}-\frac{2}{5}x=-\frac{3}{4}\times 15-\frac{3}{4}x$$

Express -\frac{3}{4}\times 15 as a single fraction.

$$-\frac{23}{5}-\frac{2}{5}x=\frac{-3\times 15}{4}-\frac{3}{4}x$$

Multiply -3 and 15 to get -45.

$$-\frac{23}{5}-\frac{2}{5}x=\frac{-45}{4}-\frac{3}{4}x$$

Fraction \frac{-45}{4} can be rewritten as -\frac{45}{4} by extracting the negative sign.

$$-\frac{23}{5}-\frac{2}{5}x=-\frac{45}{4}-\frac{3}{4}x$$

Add \frac{3}{4}x to both sides.

$$-\frac{23}{5}-\frac{2}{5}x+\frac{3}{4}x=-\frac{45}{4}$$

Combine -\frac{2}{5}x and \frac{3}{4}x to get \frac{7}{20}x.

$$-\frac{23}{5}+\frac{7}{20}x=-\frac{45}{4}$$

Add \frac{23}{5} to both sides.

$$\frac{7}{20}x=-\frac{45}{4}+\frac{23}{5}$$

Least common multiple of 4 and 5 is 20. Convert -\frac{45}{4} and \frac{23}{5} to fractions with denominator 20.

$$\frac{7}{20}x=-\frac{225}{20}+\frac{92}{20}$$

Since -\frac{225}{20} and \frac{92}{20} have the same denominator, add them by adding their numerators.

$$\frac{7}{20}x=\frac{-225+92}{20}$$

Add -225 and 92 to get -133.

$$\frac{7}{20}x=-\frac{133}{20}$$

Multiply both sides by \frac{20}{7}, the reciprocal of \frac{7}{20}.

$$x=-\frac{133}{20}\times \frac{20}{7}$$

Multiply -\frac{133}{20} times \frac{20}{7} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-133\times 20}{20\times 7}$$

Cancel out 20 in both numerator and denominator.

$$x=\frac{-133}{7}$$

Divide -133 by 7 to get -19.

$$x=-19$$