Solve 2x+1/3-1geq3+5x/4

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

Solve for x

$$x\leq -\frac{17}{7}$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 3,4. Since 12 is positive, the inequality direction remains the same.

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

Use the distributive property to multiply 4 by 2x+1.

$$8x+4-12\geq 3\left(3+5x\right)$$

Subtract 12 from 4 to get -8.

$$8x-8\geq 3\left(3+5x\right)$$

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

$$8x-8\geq 9+15x$$

Subtract 15x from both sides.

$$8x-8-15x\geq 9$$

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

$$-7x-8\geq 9$$

Add 8 to both sides.

$$-7x\geq 9+8$$

Add 9 and 8 to get 17.

$$-7x\geq 17$$

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

$$x\leq -\frac{17}{7}$$