Solve 0.9(7x+6)geq1.7-(x+6)

$$0.9 ( 7 x + 6 ) \geq 1.7 - ( x + 6 )$$

Solve for x

$$x\geq -\frac{97}{73}$$

Solution Steps

Use the distributive property to multiply 0.9 by 7x+6.

$$6.3x+5.4\geq 1.7-\left(x+6\right)$$

To find the opposite of x+6, find the opposite of each term.

$$6.3x+5.4\geq 1.7-x-6$$

Subtract 6 from 1.7 to get -4.3.

$$6.3x+5.4\geq -4.3-x$$

Add x to both sides.

$$6.3x+5.4+x\geq -4.3$$

Combine 6.3x and x to get 7.3x.

$$7.3x+5.4\geq -4.3$$

Subtract 5.4 from both sides.

$$7.3x\geq -4.3-5.4$$

Subtract 5.4 from -4.3 to get -9.7.

$$7.3x\geq -9.7$$

Divide both sides by 7.3. Since 7.3 is positive, the inequality direction remains the same.

$$x\geq \frac{-9.7}{7.3}$$

Expand \frac{-9.7}{7.3} by multiplying both numerator and the denominator by 10.

$$x\geq \frac{-97}{73}$$

Fraction \frac{-97}{73} can be rewritten as -\frac{97}{73} by extracting the negative sign.

$$x\geq -\frac{97}{73}$$