Solve It
3/x = 5
Solve the following equation using algebra tiles:
2x = 6 - x
2(x + 1.5) = 6
2(x) + 2(1.5) = 6
2x + 3 = 6
2x + 3 - 3 = 6
2x = 6
2x/2 = 6/2
x = 3
Answer: x = 3/2
Half a number plus 5 is 11.
Write an equation representing this situation and solve the problem.
x/3 + 5 = 11
x = 12
3x/4 - 5/8 = 2
2x = 7
==> x = 7/2
x/4 + 1 = 5
Use the Balance Scale Model and solve the equation:
4x = 3 - 2x
Find the mistake in the following solution and fix it:
3 - x/4 = 7
3 - x/4 -3 = 7 - 3
x/4 = 4
x = 16
Answer: x = -16
Ahmed buys some shoes online for $23.00 per pair including tax, and the shipping is $5.00. If he decides to buy more pairs of those same shoes and it doesn't change the shipping cost, how many can he buy with $120.00?
Write an equation representing this situation and solve the problem.
Answer: Ahmed can buy 5 pairs of shoes.
23x + 5 = 120
Simplify the following equation so that it contains no decimals or fractions.
x/3 - 1/4 = 5
4x = 63
==> x = 63/4
Solve and Verify:
4(a - 3) = 10
Use the Balance Scale Model and solve the equation:
3(x -1) = 5
Find the mistake in the following solution and fix it:
-2(x - 3) = 15
-2(x) - 2(-3) = 15
-2x - 6 = 15
-2x - 6 + 6 = 15 + 6
-2x = 21
-2x/-2 = 21/-2
x = -21/2
Answer: x = -9/2
Maria bought notebooks for 3 dollars each and pens for 2 dollars each. She bought 5 more pens than notebooks. If she spent $40, how many notebooks and pens did Maria buy?
Write an equation representing this situation and solve the problem.
3x + 2(x+5) = 40
Simplify the following equation so that it contains no decimals or fractions.
3 - 1.3x = 6.9
x = -3
Solve and Verify:
3b + 5 = 6b - 1
Solve the following equation using algebra tiles:
-3(x - 2) = -6
Find the mistake in the following solution and fix it:
2(3x -6) = 3(5 -x)
6x - 12 = 15 - 3x
3x - 12 = 15
3x = 27
x = 9
Answer: x = 3
The sum of two numbers is 25. One of the numbers exceeds the other by 9. Find the numbers.
Write an equation representing this situation and solve the problem.
x + (x + 9) = 25
x = 8
Simplify the following equation so that it contains no decimals or fractions.
7x/9 + 3 = x/3
Solve and Verify:
2(2x + 1) = 3(x -4)
Use the Balance Scale Model and solve the equation:
2(x + 3) = -1(3x + 2)
Find the mistake in the following solution and fix it:
(3x -1)/2 = x + 5
2(3x -1)/2 = x + 5
3x - 1 = x + 5
3x - 1 + 1 = x + 5 + 1
3x = x + 6
3x - x = x + 6 - x
2x = 6
x = 3
Answer: x = 11
Peter has six times as many dimes as quarters in her piggy bank. He has $2.55 coins in his piggy bank. How many of each type of coin does she have?
Write an equation representing this situation and solve the problem.
Answer: Peter has 3 quarters and 18 dimes.
25x + 10(6x) = 255
x = 3
Simplify the following equation so that it contains no decimals or fractions.
2.4 - 0.8x = 3.6x + 1.2
4x = 1
==> x = 1/4