Solve 11.5+4.5(x+1.8)leqx

$$11.5 + 4.5 ( x + 1.8 ) \leq x$$

Solve for x

$$x\leq -5.6$$

Solution Steps

Use the distributive property to multiply 4.5 by x+1.8.

$$11.5+4.5x+8.1\leq x$$

Add 11.5 and 8.1 to get 19.6.

$$19.6+4.5x\leq x$$

Subtract x from both sides.

$$19.6+4.5x-x\leq 0$$

Combine 4.5x and -x to get 3.5x.

$$19.6+3.5x\leq 0$$

Subtract 19.6 from both sides. Anything subtracted from zero gives its negation.

$$3.5x\leq -19.6$$

Divide both sides by 3.5. Since 3.5 is positive, the inequality direction remains the same.

$$x\leq \frac{-19.6}{3.5}$$

Expand \frac{-19.6}{3.5} by multiplying both numerator and the denominator by 10.

$$x\leq \frac{-196}{35}$$

Reduce the fraction \frac{-196}{35} to lowest terms by extracting and canceling out 7.

$$x\leq -\frac{28}{5}$$