Solve 2x+3/5leq3x+1/4

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

Solve for x

$$x\geq 1$$

Solution Steps

Multiply both sides of the equation by 20, the least common multiple of 5,4. Since 20 is positive, the inequality direction remains the same.

$$4\left(2x+3\right)\leq 5\left(3x+1\right)$$

Use the distributive property to multiply 4 by 2x+3.

$$8x+12\leq 5\left(3x+1\right)$$

Use the distributive property to multiply 5 by 3x+1.

$$8x+12\leq 15x+5$$

Subtract 15x from both sides.

$$8x+12-15x\leq 5$$

Combine 8x and -15x to get -7x.

$$-7x+12\leq 5$$

Subtract 12 from both sides.

$$-7x\leq 5-12$$

Subtract 12 from 5 to get -7.

$$-7x\leq -7$$

Divide both sides by -7. Since -7 is negative, the inequality direction is changed.

$$x\geq \frac{-7}{-7}$$

Divide -7 by -7 to get 1.

$$x\geq 1$$