Solve 12/5x-4geq5/2(x-3)

$$\frac { 12 } { 5 } x - 4 \geq \frac { 5 } { 2 } ( x - 3 )$$

Solve for x

$$x\leq 35$$

Solution Steps

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

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

Express \frac{5}{2}\left(-3\right) as a single fraction.

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

Multiply 5 and -3 to get -15.

$$\frac{12}{5}x-4\geq \frac{5}{2}x+\frac{-15}{2}$$

Fraction \frac{-15}{2} can be rewritten as -\frac{15}{2} by extracting the negative sign.

$$\frac{12}{5}x-4\geq \frac{5}{2}x-\frac{15}{2}$$

Subtract \frac{5}{2}x from both sides.

$$\frac{12}{5}x-4-\frac{5}{2}x\geq -\frac{15}{2}$$

Combine \frac{12}{5}x and -\frac{5}{2}x to get -\frac{1}{10}x.

$$-\frac{1}{10}x-4\geq -\frac{15}{2}$$

Add 4 to both sides.

$$-\frac{1}{10}x\geq -\frac{15}{2}+4$$

Convert 4 to fraction \frac{8}{2}.

$$-\frac{1}{10}x\geq -\frac{15}{2}+\frac{8}{2}$$

Since -\frac{15}{2} and \frac{8}{2} have the same denominator, add them by adding their numerators.

$$-\frac{1}{10}x\geq \frac{-15+8}{2}$$

Add -15 and 8 to get -7.

$$-\frac{1}{10}x\geq -\frac{7}{2}$$

Multiply both sides by -10, the reciprocal of -\frac{1}{10}. Since -\frac{1}{10} is negative, the inequality direction is changed.

$$x\leq -\frac{7}{2}\left(-10\right)$$

Express -\frac{7}{2}\left(-10\right) as a single fraction.

$$x\leq \frac{-7\left(-10\right)}{2}$$

Multiply -7 and -10 to get 70.

$$x\leq \frac{70}{2}$$

Divide 70 by 2 to get 35.

$$x\leq 35$$