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Algebra 1
Section 1.5
Equations and Inequalities
Equation
- is formed when an equal sign is placed between two
algebraic expressions
Examples:
x–2=3
3x = 27
5x – 6 = x2 + 8
To check an equation, substitute the possible solution into the
equation for the variable. If the resulting statement is true,
then the number substituted in is a solution to the equation.
For example: Check whether the numbers 2, 3, and 4 are
solutions to the equation 3x – 1 = 11.
x
2
3
4
substitution
3(2) – 1 = 11
3(3) – 1 = 11
3(4) – 1 = 11
conclusion
2 is not a solution
3 is not a solution
4 is a solution
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Check whether the given number is a solution to the equation.
1. 3x + 1 = 13, 4
3(4) + 1 = 13
12 + 1 = 13
13 = 13
yes
4 is a solution
2. 4y + 2 = 2y + 8, 3
4(3) + 2 = 2(3) + 8
12 + 2 = 6 + 8
14 = 14
yes
3 is a solution
3. 5x – 2 = 11, 2
5(2) – 2 = 11
10 – 2 = 11
8  11
no
2 is not a solution
4. x3 = 27, 2
23 = 27
8 27
no
2 is not a solution
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Inequality
- is formed when an inequality symbol is placed between
two algebraic expressions.
Examples: 3x + 2  8
2x < 10
x2 > 6
Inequality Symbol
<
>


Meaning
is less than
is greater than
is less than or equal to
is greater than or equal to
Check whether the given number is a solution to the inequality.
6. 6 + 2x  10, 2
5. x – 2 < 6, 7
6 + 2(2)  10
7–2<6
6 + 4  10
5<6
10  10
yes
yes
7 is a solution
2 is a solution to
to the inequality
the inequality
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7. 4x – 3 <0, 1
4(1) – 3 <0
4 – 3 <0
1 <0
no
1 is not a solution
to the inequality
8. 2x2 – 3  15, 2
2(2)2 – 3 
2(4)– 3 15
8 – 3 
5 
no
2 is not a solution
to the inequality
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Check whether the given number is a solution
to the equation or inequality.
9. x2 – 10 > 16 , 6
62 – 10 > 16
36 – 10 > 16
26 > 16
yes
6 is a solution
to the inequality
10. 10  x  12 , 14
7
10  14  12
7
10 + 2 = 12
12 = 12
yes
14 is a solution
to the equation
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What is the average speed of a runner who completes
a 10,000 meter race in 25 minutes?
D = rt
10,000 = r(25)
r = 400 m/min
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You are going on a trip with some friends and you have $85 to help
pay for gas. It costs $22 to fill the tank. How many times can you
completely fill the tank? How much money will you have left?
If this problem is represented by the equation 22x + y = 85, what do
the 22, the x, the y, and the 85 represent?
22
x
y
85
dollar cost of a tank of gas
number of times you can fill the tank
dollar amount left
dollar amount available
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Algebra 1
Section 1.5
Assignment
Check whether the given number is a solution of the equation.
1.) 3 + 2x = 9, 2
3.) 6x – 4 = 3, 1
2.) 2y + y = 2y + 5, 5
Solve the equation.
4.) x + 6 = 11
5.) x – 5 = 1
6.) 2x = 6
7.) x  5
4
8.) 2x – 1 = 9
9.) x3 = 1
Check whether the given number is a solution of the inequality.
10.) 5 + x > 8, 4
11.) 3x – 1 ≥ 7, 3
12.) x – 7 ≥ 11 – x, 9
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