Writing Equations With Variables On Both Sides Worksheet Answers
SOLVING EQUATIONS WITH VARIABLES ON BOTH SIDES WORKSHEET
Problem 1 :
Solve for x :
3x - 1 = x + 5
Problem 2 :
Solve for k :
5(k - 3) - 7(6 - k) = 24 - 3(8 - k) - 3
Problem 3 :
Solve for x :
(x + 15)(x - 3) - (x2 - 6x + 9) = 30 - 15(x - 1)
Problem 4 :
Solve the following equation :
(1/2)(8y - 6) = 5y - (y + 3)
Problem 5 :
Solve the following equation :
2(1 - x) + 5x = 3(x + 1)
Problem 6 :
David's Rental Car charges an initial fee of $20 plus an additional $30 per day to rent a car. Alex's Rental Car charges an initial fee of $36 plus an additional $28 per day. For what number of days is the total cost charged by both of them the same ?
Detailed Answer Key
Problem 1 :
Solve for x :
3x - 1 = x + 5
Solution :
3x - 1 = x + 5
Subtract x from each side.
2x - 1 = 5
Add 1 to each side.
2x = 6
Divide each side by 2.
x = 3
Problem 2 :
Solve for k :
5(k - 3) - 7(6 - k) = 24 - 3(8 - k) - 3
Solution :
5(k - 3) - 7(6 - k) = 24 - 3(8 - k) - 3
Use distributive property.
5k - 15 - 42 + 7k = 24 - 24 + 3k - 3
Simplify.
12k - 57 = 3k - 3
Subtract 3k from each side.
9k - 57 = -3
Add 57 to each side.
9k = 54
Divide each side by 9.
k = 6
Problem 3 :
Solve for x :
(x + 15)(x - 3) - (x2 - 6x + 9) = 30 - 15(x - 1)
Solution :
(x + 15)(x - 3) - (x 2 - 6x + 9) = 30 - 15(x - 1)
Simplify.
x2 + 12x - 45 - x2 + 6x - 9 = 30 - 15x + 15
18x - 54 = -15x + 45
Add 15x to each side.
33x - 54 = 45
Add 54 to each side.
33x = 99
Divide each side by 33.
x = 3
Problem 4 :
Solve the following equation :
(1/2)(8y - 6) = 5y - (y + 3)
Solution :
(1/2)(8y - 6) = 5y - (y + 3)
Simplify both sides.
4y - 3 = 5y - y - 3
4y - 3 = 4y - 3
Subtract 4y from each side.
-3 = -3
The above result is true. Because the result we get at the last step is true, the given equation has infinitely has many solutions.
Problem 5 :
Solve the following equation :
2(1 - x) + 5x = 3(x + 1)
Solution :
2(1 - x) + 5x = 3(x + 1)
Simplify both sides.
2 - 2x + 5x = 3x + 3
2 + 3x = 3x + 3
Subtract 3x from each side.
2 = 3
The above result is false. Because 2 is not equal to 3. Because the result we get at the last step is false, the given equation has no solution.
Problem 6 :
David's Rental Car charges an initial fee of $20 plus an additional $30 per day to rent a car. Alex's Rental Car charges an initial fee of $36 plus an additional $28 per day. For what number of days is the total cost charged by both of them the same ?
Solution :
Let 'x' be the number of days for which the total cost charged by both of them is same.
Step 1 :
Write an expression using 'x' representing the total cost of renting a car from David's Rental Car.
Total cost = Initial fee + cost for "x" days
Total days = 20 + 30x
Step 2 :
Write an expression using 'x' representing the total cost of renting a car from Alex's Rental Car.
Total cost = Initial fee + cost for 'x' days
Total days = 36 + 28x
Step 3 :
We have assumed that the total cost charged by both of them is same for 'x' number of days.
So, we have
20 + 30x = 36 + 28x
Step 4 :
Solve for 'x'.
20 + 30x = 36 + 28x
Subtract 28x from each side.
20 + 2x = 36
Subtract 20 from each side.
2x = 16
Divide each side by 2.
x = 8
So, the total cost charged by both of them is same for 8 days.
Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.
If you have any feedback about our math content, please mail us :
v4formath@gmail.com
We always appreciate your feedback.
You can also visit the following web pages on different stuff in math.
WORD PROBLEMS
HCF and LCM word problems
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Algebra word problems
Word problems on trains
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on unit price
Word problems on unit rate
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Double facts word problems
Trigonometry word problems
Percentage word problems
Profit and loss word problems
Markup and markdown word problems
Decimal word problems
Word problems on fractions
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Time and work word problems
Word problems on sets and venn diagrams
Word problems on ages
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Profit and loss shortcuts
Percentage shortcuts
Times table shortcuts
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
Sum of all three four digit numbers formed using 0, 1, 2, 3
Sum of all three four digit numbers formed using 1, 2, 5, 6
Writing Equations With Variables On Both Sides Worksheet Answers
Source: https://www.onlinemath4all.com/solving-equations-with-variables-on-both-sides-worksheet.html
Posted by: albashignigho.blogspot.com
0 Response to "Writing Equations With Variables On Both Sides Worksheet Answers"
Post a Comment