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Chapter 6: Problem 50

Solve each inequality and graph the solution set on a number line. \(4 x-7>9 x-2\)

Short Answer

Expert verified
The solution to the inequality is \( x < -1 \) . It represents all the numbers on the number line which are less than -1.

Step by step solution

01

Isolate x coefficients

Start by gathering the x terms on one side and the constants on the other. You obtain \(4 x - 9 x > -2 +7\).
02

Simplify inequality

Subtract to simplify the left side and add to simplify the right side, which yields \(-5 x > 5\).
03

Solve for x

To solve for x, divide both sides by -5, but remember when dividing by negative number, the direction of inequality changes. This gives \( x < -1\)
04

Graph the solution

On a number line, the solution set will be everything to the left of -1. Your graph should have an open circle at -1 (since x can't be exactly -1) and an arrow pointing to the left to represent all the numbers less than -1.

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Most popular questions from this chapter

Describe ways in which solving a linear inequality is different than solving a linear equation.

Solve the quadratic equations by factoring. \(x^{2}-2 x-15=0\)

Solve the equations using the quadratic formula. \(x^{2}-3 x=10\)

Solve each equation by the method of your choice. \(x(x+1)=4-(x+2)(x+2)\)

Use FOIL to find the products. \((3 x-7)(4 x-5)\)
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