Variables on Each Side
The equation 3 x + 6 = 4 x + 3 represents the cost in dollars, x, of a school lunch. Solve the equation. Write the solution as a whole number or decimal.
x=3
Solve: 4(2x−2)+6x=5(3x−2)−7
x=9
Dean wants to have a laptop case shipped to his office. Company A charges a $10 shipping fee and $2 per pound. Company B charges a $12 shipping fee and $1.50 per pound. For how many pounds is the cost of both shipping companies the same?
Write an equation that represents the problem, where p is the number of pounds of the package.
10 + 2p = 12 + 1.5p
Determine whether the equation has one solution, no solution, or infinitely many solutions.
4(x-8)+12=2(2x-9)
No solution
What value of x makes this equation 11^-6/11^2=(11^4)^x true?
a. -3
b. -2
c. 1
d. 8
b. -2
Solve −2.7x+3.5=1.3x+11.5 Write the solution as an integer or decimal.
x= -2
Solve: -5(2x+3)-x=4(x+11)+1
x=-4
Two companies offer Elizabeth a sales position. Company A pays $3,500 per month plus $275 per car sold. Company B pays $3,000 per month plus $350 per car sold. Write an equation that could be used to determine the number of cars sold in a month, x, that would result in the same total income from each company?
3 , 500 + 275 x = 3 , 000 + 350 x
What value of coefficient b makes the equation a no solution
5x−2(3x+6)=bx-16
b=-1
The average mass of an ant is 4.5 xx 10^-3 . If the approximate mass of all the ants in the world is 4.41 xx 10^12 grams, approximately how many ants are in the world?
9.8 xx 10^14
Consider the equation −0.25a+3.8=0.5a−5.2
Solve the equation. Write the solution as an integer or decimal.
a= 12
Solve 0.1(x+6)−0.7x=0.4(2x−2)+8.4
x=-5
The temperature of one furnace is 1,400°C and cools at a rate of 25°C per minute. The temperature of another furnace is 1,200°C and is heated at a rate of 15°C per minute. After how many minutes will the furnaces be the same temperature? Write and solve an equation to model the problem.
1,400-25x=1,200+15x
5 Minutes
What value of coefficient b makes the equation true for any real number x?
-2( 4x - 3 ) + 5x = bx+6
b=-3
Which fraction is equivalent to 0. overline36 ?
a. 17/50
b. 7/20
c. 9/25
d. 4/11
d.
4/11
The equation 4/5d−5=3/5d−2 represents the number of dimes, dd, in a stack. Solve the equation. Write the solution as a whole number.
d=15
Solve: 1/2(6x-4)+6x=-12(1/6x+2)
x=-2
Eric and Willow collect baseball cards. Eric has 350 baseball cards and collects 10 cards per week. Willow has 250 baseball cards and collects 15 cards per week. After how many weeks will Eric and Willow have the same number of baseball cards? Write and solve the equation.
350+10x=250+15x
x=20
Which statement about the equation is true?
6(d+10) = 4(d−18)
a. The equation has precisely one solution
b. The equation has precisely two solutions
c. The equation has infinitely solutions
d. The equation has no solutions.
a. The equation has precisely one solution
Consider the set of numbers.
6/pi, 2sqrt 6, 2pi, sqrt 8
When plotted on a horizontal number line, which is ordered from least to greatest?
6/pi, sqrt 8, 2sqrt6, 2pi
Consider the equation
7/9x-6=8/9x-10
Solve the equation. Write the solution as an integer or decimal.
x= 36
What value of y satisfies the equation
2/3( y + 6) = 1/3y + 7
y=9
Ms. Davenport purchased 5 tickets to a play, each ticket with the same price. She was also charged an online service fee of $3.50 per ticket. Mrs. Follett purchased 3 tickets to the same play and paid twice as much for her tickets as Ms. Davenport. Mrs. Follett was also charged a service fee of $2.75 per ticket. If they spent the same amount, what is the total cost of each tickets Ms. Davenport purchased?
5(x+3.5)=3(2x+2.75)
x=9.25
Determine whether each equation has one solution, no solution, or infinitely many solutions.
2(5x+3)=6(x+8)+2
4(x−5)=2(9+2x)
3(4x−4)=4(3x−3)
2(5x+3)=6(x+8)+2: One Solution
4(x−5)=2(9+2x): No Solution
3(4x−4)=4(3x−3): Infinite
The area of a square is 81 square centimeters. To find the side length of the square, a student correctly solves the equation s^2=81 , where s represents the side length of one side of the square. What is the perimeter of the square?
a. 9 cm
b. 18 cm
c. 36 cm
d. 162 cm
c.36 cm