Solve 2/3x+5geq1/4-2x

$$\frac { 2 } { 3 } x + 5 \geq \frac { 1 } { 4 } - 2 x$$

Solve for x

$$x\geq -\frac{57}{32}$$

Solution Steps

Add 2x to both sides.

$$\frac{2}{3}x+5+2x\geq \frac{1}{4}$$

Combine \frac{2}{3}x and 2x to get \frac{8}{3}x.

$$\frac{8}{3}x+5\geq \frac{1}{4}$$

Subtract 5 from both sides.

$$\frac{8}{3}x\geq \frac{1}{4}-5$$

Convert 5 to fraction \frac{20}{4}.

$$\frac{8}{3}x\geq \frac{1}{4}-\frac{20}{4}$$

Since \frac{1}{4} and \frac{20}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8}{3}x\geq \frac{1-20}{4}$$

Subtract 20 from 1 to get -19.

$$\frac{8}{3}x\geq -\frac{19}{4}$$

Multiply both sides by \frac{3}{8}, the reciprocal of \frac{8}{3}. Since \frac{8}{3} is positive, the inequality direction remains the same.

$$x\geq -\frac{19}{4}\times \frac{3}{8}$$

Multiply -\frac{19}{4} times \frac{3}{8} by multiplying numerator times numerator and denominator times denominator.

$$x\geq \frac{-19\times 3}{4\times 8}$$

Do the multiplications in the fraction \frac{-19\times 3}{4\times 8}.

$$x\geq \frac{-57}{32}$$

Fraction \frac{-57}{32} can be rewritten as -\frac{57}{32} by extracting the negative sign.

$$x\geq -\frac{57}{32}$$