Operations
x+7=15
Show Work
x=8
Does x=3 make the equation x+4=7
true?
Show substitution.
Yes.
3+4=7
Maria has 8 pencils. She gets some more and now has 13. Write an equation.
x+8=13 or 8+x=13
x+1.4=3.4
x=2.0
Write an inequality to represent: "x is less than 8." Then state whether 6 is a solution or not.
x<8
Yes 6 is a solution
6x=24
Show Work
x=4
Does x=12 make 4x=2 true.
Show substitution.
No. 4(12) does not equal 12.
A box holds 9 apples in each layer. There are x and 27 apples total. Write an equation.
9x=27
0.5x=2.0
x=4
Write an inequality for: "A student must score more than 70 points to pass." Let x be the student's score. Represent the solution set on a number line (describe where the shading would be).
x>70
x+19=32
Show Work
x=13
Determine if x=0.75 satisfies x+1.25=2.0
Show substitution.
Yes. 0.75+1.25+2.0
A toy costs $12 after a friend gives $5 toward it. How much did Erin pay, let x be the amount Erin paid. Write and solve an equation.
12=5+x
x=7
x+1.75=3.25
x=1.5
Write and solve an inequality for: "A parking lot has room for fewer than 50 cars; write an inequality for the number of cars x allowed." Explain whether 49 and 50 are solutions.
X<50
49 is a solution.
50 is not a solution.
8x=56
Show Work
For the equation 7x=21, use substitution to test whether x=3 and whether x=2
are solutions. Show work.
Yes x=3
7(2)=14, not 21. 2 is not a solution.
A recipe uses a 3 cups of sugar per batch. If you want 2 batches, how much sugar is needed, let x be the total cups of sugar. Write and solve an equation.
x/3=2
x=6
25x=65
Show work
x=2.6
Write an inequality to represent: "You must save at least $20 to buy a game." Let x be money saved. State whether 20 and 19.99 satisfy the inequality. Describe the solution on a number line.
x>_20
20 is a solution.
19.99 is not a solution.
x+125=348
Show Work
x=223
Given the set {1, 2, 3, 4, 5}, which values (if any) make x+3=7 true? Use substitution to justify.
4 makes x+3=7 true.
4+3=7
A landscaper charges $15 per square foot to mow. If the mowing job costs $180, how many square feet are in the yard, let x be the number of square feet. Write an equation and solve.
15x=180
x=12
0.25x+0=1.5
Show work
x=6
Create an inequality from this context: "A baker can bake at most 120 cookies in a day. Let x be cookies baked." Write the inequality, then explain why there are infinitely many solutions and give three example integer solutions.
x<_120
Every number less than 120 and including 120.
Three solutions are: 119, 2, 78