Solve 5(2-3x)+4(3x+5)leq2(-x+1)

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

Solve for x

$$x\geq 28$$

Solution Steps

Use the distributive property to multiply 5 by 2-3x.

$$10-15x+4\left(3x+5\right)\leq 2\left(-x+1\right)$$

Use the distributive property to multiply 4 by 3x+5.

$$10-15x+12x+20\leq 2\left(-x+1\right)$$

Combine -15x and 12x to get -3x.

$$10-3x+20\leq 2\left(-x+1\right)$$

Add 10 and 20 to get 30.

$$30-3x\leq 2\left(-x+1\right)$$

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

$$30-3x\leq 2\left(-x\right)+2$$

Subtract 2\left(-x\right) from both sides.

$$30-3x-2\left(-x\right)\leq 2$$

Multiply -1 and 2 to get -2.

$$30-3x-2\left(-1\right)x\leq 2$$

Multiply -2 and -1 to get 2.

$$30-3x+2x\leq 2$$

Combine -3x and 2x to get -x.

$$30-x\leq 2$$

Subtract 30 from both sides.

$$-x\leq 2-30$$

Subtract 30 from 2 to get -28.

$$-x\leq -28$$

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

$$x\geq \frac{-28}{-1}$$

Fraction \frac{-28}{-1} can be simplified to 28 by removing the negative sign from both the numerator and the denominator.

$$x\geq 28$$