Solve 2(1.5x-2.1)+1.7geq2(2.4x-3.5)

$$2 ( 1.5 x - 2.1 ) + 1.7 \geq 2 ( 2.4 x - 3.5 )$$

Solve for x

$$x\leq 2.5$$

Solution Steps

Use the distributive property to multiply 2 by 1.5x-2.1.

$$3x-4.2+1.7\geq 2\left(2.4x-3.5\right)$$

Add -4.2 and 1.7 to get -2.5.

$$3x-2.5\geq 2\left(2.4x-3.5\right)$$

Use the distributive property to multiply 2 by 2.4x-3.5.

$$3x-2.5\geq 4.8x-7$$

Subtract 4.8x from both sides.

$$3x-2.5-4.8x\geq -7$$

Combine 3x and -4.8x to get -1.8x.

$$-1.8x-2.5\geq -7$$

Add 2.5 to both sides.

$$-1.8x\geq -7+2.5$$

Add -7 and 2.5 to get -4.5.

$$-1.8x\geq -4.5$$

Divide both sides by -1.8. Since -1.8 is negative, the inequality direction is changed.

$$x\leq \frac{-4.5}{-1.8}$$

Expand \frac{-4.5}{-1.8} by multiplying both numerator and the denominator by 10.

$$x\leq \frac{-45}{-18}$$

Reduce the fraction \frac{-45}{-18} to lowest terms by extracting and canceling out -9.

$$x\leq \frac{5}{2}$$