Question

Solve and graph the solution to the inequality -2(2x-3)<-26

Answer 1

Answer:

$x > 8$

Step-by-step explanation:

1. Simplify the expression

Expand the parentheses:

$-2*2x-2*-3<-26$

Simplify the arithmetic:

$-4x+6<-26$

2. Group all constants on the right side of the inequality

Subtract 6 from both sides:

$-4x+6-6<-26-6$

Simplify the arithmetic:

$-4x<-26-6$

Simplify the arithmetic:

$-4x<-32$

3. Isolate the x

Divide both sides by-4:

When dividing or multiplying by a negative number, always flip the inequality sign:

$\frac{-4x}{-4} >\frac{-32}{-4}$

Cancel out the negatives:

$\frac{4x}{4} >\frac{-32}{-4}$

Simplify the fraction:

$x>\frac{-32}{-4}$

Cancel out the negatives:

$x>\frac{32}{4}$

Find the greatest common factor of the numerator and denominator:

$x>\frac{8*4}{1*4}$

Factor out and cancel the greatest common factor:

$x>8$

4. Solution on a coordinate plane

Solution:

$x>8$

Interval notation:

$(8, { \infty} )$