Solve 7-2*(x+1)leqx/3+2*(3-x)

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

Solve for x

$$x\geq -3$$

Solution Steps

Multiply both sides of the equation by 3. Since 3 is positive, the inequality direction remains the same.

$$21-6\left(x+1\right)\leq x+6\left(3-x\right)$$

Use the distributive property to multiply -6 by x+1.

$$21-6x-6\leq x+6\left(3-x\right)$$

Subtract 6 from 21 to get 15.

$$15-6x\leq x+6\left(3-x\right)$$

Use the distributive property to multiply 6 by 3-x.

$$15-6x\leq x+18-6x$$

Combine x and -6x to get -5x.

$$15-6x\leq -5x+18$$

Add 5x to both sides.

$$15-6x+5x\leq 18$$

Combine -6x and 5x to get -x.

$$15-x\leq 18$$

Subtract 15 from both sides.

$$-x\leq 18-15$$

Subtract 15 from 18 to get 3.

$$-x\leq 3$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x\geq -3$$