Basic Examples
If x=5, what is the value of 2x+3?
2(5)+3=10+3=13
A concert ticket costs pp dollars. If p=25, how much do 3 tickets cost?
75 dollars
Problem: If x=3x=3, evaluate 5x−25x−2.
Student's Work: 5(3)−2=15+2=17.
What’s the mistake?
The student added instead of subtracted. The correct solution is:5(3)−2=15−2=13
A train is moving at a speed of ss miles per hour. If s=60, how far does it travel in 3 hours?
60x3=180 miles
If a=−3, evaluate 4a−7?
4(−3)−7=−12−7=−19
A taxi charges 2+0.75m dollars for a ride, where m is the number of miles. If you travel 10 miles, how much do you pay?
2+0.75(10)=$9.50
Problem: If a=−2, evaluate 3a^2+4.
Student's Work:3(−2^2)+4=3(−4)+4=−12+4=−8
What’s the mistake?
3((−2)^2)+4=3(4)+4=12+4=16.
The area of a triangle is given by A=1/2bh. If b=10 and h=8, find A.
A=1/2(10)(8)=40
If n=3, what is the value of 4(n+5)
4(3+5)=32
A rectangle's perimeter is given by P=2l+2w. If l=8 and w=5, find the perimeter.
2(8)+2(5)=16+10=26
Solve for x when y=2x+1y=2x+1 and y=9.
Student's Work: 9=2x+1
2x=9+1
2x=10
x=5
What's the mistake?
The student added instead of subtracting. The correct solution is: 2x=9−1, 2x=8, x=4
John has twice as many marbles as Sam. If Sam has m marbles and m=6, how many does John have?
2(6)=12 marbles
If t=3 and v=5, what is the value of 5t-v?
5(3)-5=10
A cell phone plan costs 40+0.05d dollars per month, where dd is the number of texts sent. If you send 200 texts, how much is the bill?
40+0.05(200)=40+10=$50
If b=5, evaluate 4b−6.
Student's Work:
4(5)−6=20+6=26
What’s the mistake?
The student added instead of subtracted. The correct solution is:4(5)−6=20−6=14.
A coffee shop charges $2 per cup of coffee and $3 per muffin. If James buys 4 muffins and 2 cups of coffee, how much was his total bill?
2(2)+3(4)=$16
If t=3, u=2, and v=5, what is the value of 3tv+8u?
3(3)(5)+8(2)=61
Sarah is filling a swimming pool using a hose that adds 8 gallons of water per minute. Before she started, there were already 50 gallons in the pool. If it takes 56 minutes for the pool to fill up, how many gallons is the pool?
498 gallons
Solve for x when y=3x−4 and y=14.
Student's Work:
14=3x−4
3x=14−4
3x=10
x=4
What’s the mistake?
The student divided incorrectly. The correct solution is: x=10/3
A car rental company charges 50+0.20m dollars, where m is the miles driven. If he drove 200 miles, how much did he pay?
50+0.20(200)=$90