Solve -2/3(x+5)-1<3

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

Solve for x

$$x>-11$$

Solution Steps

Use the distributive property to multiply -\frac{2}{3} by x+5.

$$-\frac{2}{3}x-\frac{2}{3}\times 5-1<3$$

Express -\frac{2}{3}\times 5 as a single fraction.

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

Multiply -2 and 5 to get -10.

$$-\frac{2}{3}x+\frac{-10}{3}-1<3$$

Fraction \frac{-10}{3} can be rewritten as -\frac{10}{3} by extracting the negative sign.

$$-\frac{2}{3}x-\frac{10}{3}-1<3$$

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

$$-\frac{2}{3}x-\frac{10}{3}-\frac{3}{3}<3$$

Since -\frac{10}{3} and \frac{3}{3} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{2}{3}x+\frac{-10-3}{3}<3$$

Subtract 3 from -10 to get -13.

$$-\frac{2}{3}x-\frac{13}{3}<3$$

Add \frac{13}{3} to both sides.

$$-\frac{2}{3}x<3+\frac{13}{3}$$

Convert 3 to fraction \frac{9}{3}.

$$-\frac{2}{3}x<\frac{9}{3}+\frac{13}{3}$$

Since \frac{9}{3} and \frac{13}{3} have the same denominator, add them by adding their numerators.

$$-\frac{2}{3}x<\frac{9+13}{3}$$

Add 9 and 13 to get 22.

$$-\frac{2}{3}x<\frac{22}{3}$$

Multiply both sides by -\frac{3}{2}, the reciprocal of -\frac{2}{3}. Since -\frac{2}{3} is negative, the inequality direction is changed.

$$x>\frac{22}{3}\left(-\frac{3}{2}\right)$$

Multiply \frac{22}{3} times -\frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$x>\frac{22\left(-3\right)}{3\times 2}$$

Do the multiplications in the fraction \frac{22\left(-3\right)}{3\times 2}.

$$x>\frac{-66}{6}$$

Divide -66 by 6 to get -11.

$$x>-11$$