Solve 0.4+5.7leq2.6-3left(1.2x-7right)

$$0.4+5.7 \leq 2.6-3 \left( 1.2x-7 \right)$$

Solve for x

$$x\leq \frac{175}{36}$$

Solution Steps

Add 0.4 and 5.7 to get 6.1.

$$6.1\leq 2.6-3\left(1.2x-7\right)$$

Use the distributive property to multiply -3 by 1.2x-7.

$$6.1\leq 2.6-3.6x+21$$

Add 2.6 and 21 to get 23.6.

$$6.1\leq 23.6-3.6x$$

Swap sides so that all variable terms are on the left hand side. This changes the sign direction.

$$23.6-3.6x\geq 6.1$$

Subtract 23.6 from both sides.

$$-3.6x\geq 6.1-23.6$$

Subtract 23.6 from 6.1 to get -17.5.

$$-3.6x\geq -17.5$$

Divide both sides by -3.6. Since -3.6 is negative, the inequality direction is changed.

$$x\leq \frac{-17.5}{-3.6}$$

Expand \frac{-17.5}{-3.6} by multiplying both numerator and the denominator by 10.

$$x\leq \frac{-175}{-36}$$

Fraction \frac{-175}{-36} can be simplified to \frac{175}{36} by removing the negative sign from both the numerator and the denominator.

$$x\leq \frac{175}{36}$$