Chapter A, Problem 14E

To determine

To solve the below inequality in terms of intervals and illustrate the solution set on the real number line -

  $1+5x>5-3x$

Answer to Problem 14E

The solution of the inequality is $x>\frac{1}{2}$ and the solution set on a real number line -

  

Explanation of Solution

Given: Inequality: $1+5x>5-3x$

Formula Used:

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value.

Real number line is the line whose points are the real numbers. 

Calculation:

Given: Inequality equation is $1+5x>5-3x$

Solving the above equation, we have:

Subtract $\left(-1\right)$ from both the sides -

  $1+5x-1>5-3x-1$

Solving further:

  $5x>4-3x$

Add $\left(3x\right)$ to both the sides -

  $5x+3x>4-3x+3x$

Solving further:

  $8x>4$

Divide both the sides by $\left(8\right)$ and reversing the inequality, we have:

  $\frac{8x}{8}>\frac{4}{8}$

  $x>\frac{1}{2}$

Drawing the above inequality on a real number line, we have:

  

Conclusion:

Hence, the solution of the inequality is $x>\frac{1}{2}$ and the solution set on a real number line -