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Chapter 6: Problem 54

Solve each inequality and graph the solution set on a number line. \(7-2(x-4)<5(1-2 x)\)

Short Answer

Expert verified
The solution to the inequality is \( x > 1.25 \). When graphed on a number line, this is shown as an arrow to the right of 1.25.

Step by step solution

01

Simplify both sides

Expand and simplify both sides of the inequality.The left side becomes \(7-2x+8=15\), and the right side simplifies to \(5-10x\). The inequality to solve now is \(15-2x<5-10x\).
02

Collect like terms

Transpose the equation to collect the x terms on one side and the constants on the other, which results in \( 2x - 10x < 5 - 15\). Combine like terms to simplify further to: \( -8x < -10\).
03

Solve for x

Solve for x by dividing both sides by -8. Remember that dividing by a negative number reverses the inequality symbol, therefore, \( x > 1.25 \)
04

Graph the inequality on a number line

Draw a number line, and make a mark at 1.25. Because the inequality is 'greater than', shade or draw an arrow to the right of 1.25, indicating that x can be any number greater than 1.25

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