Solve 3(x-7)/2+xleq5(x-1)/2

$$\frac { 3 ( x - 7 ) } { 2 } + x \leq \frac { 5 ( x - 1 ) } { 2 }$$

Solve for x

$$x\in \mathrm{R}$$

Solution Steps

Multiply both sides of the equation by 2. Since 2 is positive, the inequality direction remains the same.

$$3\left(x-7\right)+2x\leq 5\left(x-1\right)$$

Use the distributive property to multiply 3 by x-7.

$$3x-21+2x\leq 5\left(x-1\right)$$

Combine 3x and 2x to get 5x.

$$5x-21\leq 5\left(x-1\right)$$

Use the distributive property to multiply 5 by x-1.

$$5x-21\leq 5x-5$$

Subtract 5x from both sides.

$$5x-21-5x\leq -5$$

Combine 5x and -5x to get 0.

$$-21\leq -5$$

This is true for any x.

$$x\in \mathrm{R}$$