Two-Step Linear Equations
3x−4=8.
x=4
A group of 4 friends wants to split the cost of a meal equally. If the total bill is $32, how much will each person pay?
Equation: 4x=32, Solution: x=8
2x+3≤9
x≤3
A person can buy no more than 5 tickets to a concert, and each ticket costs $15. How much money can they spend?
Inequality: 15x≤75, Solution: x≤5
Solve and graph the solution: x+2≤ 6
Answer: x≤ 4, Graph: Solid circle at 4 with an arrow pointing towards the 3.
2x+5=17
x=6
Sarah has $15. She buys 3 pencils that each cost $2. How much money does she have left?
Equation: 15−3x=9, Solution: x=2
4x−5>7
x>3
A student needs at least 40 points on a test to pass. If they already have 18 points, how many more points do they need?
Inequality: x+18≥40, Solution: x≥22
Solve and graph the solution: 3x≥ 12
Answer: x≥ 4, Graph: Solid circle at 4 with an arrow pointing towards the 5
4x−3=9
x=3
A library charges a $5 fee plus $1 per book rented. If a person spends a total of $12, how many books did they rent?
Equation: 5+x=12, Solution: x=7
3x+2≥11
x≥3
A store sells T-shirts for $10 each. A person wants to spend no more than $50. How many shirts can they buy?
Inequality: 10x≤50, Solution: x≤5
Solve and graph the solution: 5x−3<12
Answer: x<3, Graph: Open circle at 3 with an arrow pointing towards the 2.
5(x+2)=35
x=5
John has 8 more dollars than 4 times the amount of money David has. If together they have $36, how much money does David have?
Equation: 4x+8+x=36, Solution: x=5
−5x+6<16
x>−2
A car rental company charges $20 per day. A person has no more than $120 to spend. How many days can they rent the car?
Inequality: 20x≤120, Solution: x≤6
Solve and graph the solution: 2x+1>9
Answer: x>4, Graph: Open circle at 4 with an arrow pointing towards the 4.
3(x−4)+7=19
x=6
A store is having a sale on shirts. The price of a shirt is $10. If a customer buys 3 shirts and gets a $5 discount, how much will the total cost be?
Equation: 3x−5=25, Solution: x=10
−2x+3≥9
x≤−3
A person spends $12 on snacks and has $50 left. If each snack costs $3, how many snacks can they buy?
Inequality: 3x≤38, Solution: x≤12
Solve and graph the solution: -4x−2>14.
Answer: x<-4, Graph: Open circle at -4 with an arrow pointing towards the -5.