Solve 5x+1geq2/5x+7

$$5 x + 1 \geq \frac { 2 } { 5 } x + 7$$

Solve for x

$$x\geq \frac{30}{23}$$

Solution Steps

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

$$5x+1-\frac{2}{5}x\geq 7$$

Combine 5x and -\frac{2}{5}x to get \frac{23}{5}x.

$$\frac{23}{5}x+1\geq 7$$

Subtract 1 from both sides.

$$\frac{23}{5}x\geq 7-1$$

Subtract 1 from 7 to get 6.

$$\frac{23}{5}x\geq 6$$

Multiply both sides by \frac{5}{23}, the reciprocal of \frac{23}{5}. Since \frac{23}{5} is positive, the inequality direction remains the same.

$$x\geq 6\times \frac{5}{23}$$

Express 6\times \frac{5}{23} as a single fraction.

$$x\geq \frac{6\times 5}{23}$$

Multiply 6 and 5 to get 30.

$$x\geq \frac{30}{23}$$