**Solving Equations and Inequalities by Graphing Worksheet :**

Worksheet given in this section will be much useful for the students who would like to practice problems on solving equations and inequalities by graphing.

**Problem 1 :**

Solve the following equation by graphing :

-3x + 20 = 5

**Problem 2 : **

Solve the following equation by graphing :

|x - 4| = 0.5x + 1

**Problem 3 :**

Solve the following inequality by graphing :

-3x + 20 > 5

**Problem 4 :**

Solve the following equation by graphing :

x^{2} - 4 > 0

**Problem 1 :**

Solve the following equation by graphing :

-3x + 20 = 5

**Solution : **

An equation is a statement that two expressions are equal. The values of x that make the equation true are the solutions.

To have an equation by graphing, write two new equations by setting y equal to each in the original equation.

-3x + 20 = 5

**y = -3x + 20 y = 5 **

Graph the two equations and identify the points of intersection. These points will have x-values that produce the same y-values for both expressions.

Each of the x-values is a solution to the original equation.

Graph y = -3x + 20 and y = 5.

It appears that y = -3x + 20 and y = 5 intersect at

x = 5

By substituting this value into the original equation, we can verify the result.

So, -3x + 20 = 5 when x = 5.

This is the only point on the graph where the value of the functions y = -3x + 20 and y = 5 are equal.

Hence, the solution to the equation -3x + 20 = 5 is

x = 5

**Problem 2 : **

Solve the following equation by graphing :

|x - 4| = 0.5x + 1

**Solution : **

As we have done in example 1 above, write two new equations by setting y equal to each in the original equation.

|x - 4| = 0.5x + 1

**y = |x - 4| y = 0.5x + 1 **

Graph the two equations and identify the points of intersection. These points will have x-values that produce the same y-values for both expressions.

It appears that y = |x - 4| and y = 0.5x + 1 intersect at

x = 2 and x = 10

Hence, the solutions to tBy substituting this value into the original equation, we can verify the result.

So, -3x + 20 = 5 when x = 5.

This is the only point on the graph where the value of the functions y = -3x + 20 and y = 5 are equal.

Hence, the solutions to the equations y = |x - 4| and aaaaaa y = 0.5x + 1 is

x = 2 and x = 10

**Problem 3 :**

Solve the following inequality by graphing :

-3x + 20 > 5

**Solution : **

To solve the inequality, we have to identify the values of x that make the value of the expression -3x + 20 greater than 5.

To have an inequality by graphing, write two new equations by setting y equal to each in the original inequality.

-3x + 20 > 5

**y = -3x + 20 y = 5 **

Graph the two equations and identify the points of intersection. These points will have x-values that produce the same y-values for both expressions.

Graph y = -3x + 20 and y = 5.

From the point of intersection, it is clear that y = 5 when x = 5.

In the above graph, y > 5 when x < 5.

That is,

-3x + 20 > 5 when x < 5

Hence, the solution to the inequality -3x + 20 > 5 is

x < 5 or x ∈ (-∞, 5)

**Problem 4 :**

Solve the following equation by graphing :

x^{2} - 4 > 0

**Solution : **

To solve the inequality, we have to identify the values of x that make the value of the expression x^{2} - 4 greater than 0.

Graph the equation y = x^{2} - 4 by translating the parent function y = x^{2} down 4 units.

In the above graph, y > 0 when

x < -2 and x > 2

That is, x^{2} - 4 > 0 when

x < -2 and x > 2

Hence, the solution to the inequality x^{2} - 4 > 0 is

x < -2 or x > 2

or

x ∈ (-∞, 2)U(2, ∞)

After having gone through the stuff given above, we hope that the students would have understood, how to solve equations and inequalities by graphing.

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

Widget is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**