Solve 3/2(x+4)geq2-1/5(1-4x)

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

Solve for x

$$x\geq -6$$

Solution Steps

Use the distributive property to multiply \frac{3}{2} by x+4.

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

Express \frac{3}{2}\times 4 as a single fraction.

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

Multiply 3 and 4 to get 12.

$$\frac{3}{2}x+\frac{12}{2}\geq 2-\frac{1}{5}\left(1-4x\right)$$

Divide 12 by 2 to get 6.

$$\frac{3}{2}x+6\geq 2-\frac{1}{5}\left(1-4x\right)$$

Use the distributive property to multiply -\frac{1}{5} by 1-4x.

$$\frac{3}{2}x+6\geq 2-\frac{1}{5}-\frac{1}{5}\left(-4\right)x$$

Express -\frac{1}{5}\left(-4\right) as a single fraction.

$$\frac{3}{2}x+6\geq 2-\frac{1}{5}+\frac{-\left(-4\right)}{5}x$$

Multiply -1 and -4 to get 4.

$$\frac{3}{2}x+6\geq 2-\frac{1}{5}+\frac{4}{5}x$$

Convert 2 to fraction \frac{10}{5}.

$$\frac{3}{2}x+6\geq \frac{10}{5}-\frac{1}{5}+\frac{4}{5}x$$

Since \frac{10}{5} and \frac{1}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{2}x+6\geq \frac{10-1}{5}+\frac{4}{5}x$$

Subtract 1 from 10 to get 9.

$$\frac{3}{2}x+6\geq \frac{9}{5}+\frac{4}{5}x$$

Subtract \frac{4}{5}x from both sides.

$$\frac{3}{2}x+6-\frac{4}{5}x\geq \frac{9}{5}$$

Combine \frac{3}{2}x and -\frac{4}{5}x to get \frac{7}{10}x.

$$\frac{7}{10}x+6\geq \frac{9}{5}$$

Subtract 6 from both sides.

$$\frac{7}{10}x\geq \frac{9}{5}-6$$

Convert 6 to fraction \frac{30}{5}.

$$\frac{7}{10}x\geq \frac{9}{5}-\frac{30}{5}$$

Since \frac{9}{5} and \frac{30}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{10}x\geq \frac{9-30}{5}$$

Subtract 30 from 9 to get -21.

$$\frac{7}{10}x\geq -\frac{21}{5}$$

Multiply both sides by \frac{10}{7}, the reciprocal of \frac{7}{10}. Since \frac{7}{10} is positive, the inequality direction remains the same.

$$x\geq -\frac{21}{5}\times \frac{10}{7}$$

Multiply -\frac{21}{5} times \frac{10}{7} by multiplying numerator times numerator and denominator times denominator.

$$x\geq \frac{-21\times 10}{5\times 7}$$

Do the multiplications in the fraction \frac{-21\times 10}{5\times 7}.

$$x\geq \frac{-210}{35}$$

Divide -210 by 35 to get -6.

$$x\geq -6$$