Question

find the solution set and number line of 5-4x < 10-x

Answer 1

5-10<4x-x
-5<3x
x>-5/3

Answer 2

Solution set of inequality is all the values greater than -5/3 or -1.67.

In interval notation (-5/3,∞)

Given:

$5 - 4x < 10 - x$

To find:

• Find the solution set and represent on number line.

Solution:

Step 1:

Add x in both sides of inequality.

$5 - 4x + x < 10 - x + x$

or

$5 - 3x < 10$

Step 2:

Subtract 5 from both sides.

$- 3x < 5$

or

Multiply (-1), multiplication with -1 changes the sign of inequality.

$3x > -5$

or

$\bf \red{ x > - \frac{5}{3} }$

Thus,

Solution set of inequality is all the values greater than -5/3 or -1.67.

In interval notation (-5/3,∞)

*Representation on number line is attached.

Learn more:

1) solve the following inequality and write the solution set using interval notation

1. -9<2x+7<_19

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2) Graph the solution set to this inequality. 3x - 11 > 7x + 9

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