What is the first step in solving the equation 20 = 6x − 4 solving for x?(1 point)

Question

Responses

Add 4 to both sides.
Add 4 to both sides.

Subtract 20 from both sides.
Subtract 20 from both sides.

Subtract 4 from both sides.
Subtract 4 from both sides.

Divide both sides by 6.

Shawnece is solving the equation x/7 − 4 = −6. One of her steps is to multiply both sides of the equation by 7. Why? (1 point)
Responses

Multiplying both sides by 7 undoes the addition in the original problem.
Multiplying both sides by 7 undoes the addition in the original problem.

The negative sign in −6 must be changed to positive.
The negative sign in negative 6 must be changed to positive.

Multiplying both sides by 7 undoes the division of x
by 7 in the original problem.
Multiplying both sides by 7 undoes the division of x by 7 in the original problem.

Multiplying both sides by 7 undoes the subtraction in the original problem.

Tillie is solving an equation for x
. Her first step is to subtract 8 from both sides of the equation. Which equation is she solving?(1 point)
Responses

12 − x = −8
12 minus x equals negative 8

12 = −x − 8
12 equals negative x minus 8

12 − x = 8
12 minus x equals 8

12 = −x + 8

What is the first step in solving the equation 12(x + 7) = 0 for x?(1 point)
Responses

Divide both sides by 12.
Divide both sides by 12.

Subtract 7 from both sides.
Subtract 7 from both sides.

Multiply both sides by 12.
Multiply both sides by 12.

Add 7 to both sides.

What is the solution to the equation 0.24(x−10.2)=6 when solving for x?(1 point)
Responses

35.2
35.2

11.64
11.64

16.44
16.44

14.8

Solve for x in the equation 8/11(x+4/5)=24/55 .

What is the solution to the equation 1.26(x−7.352)=6.426 when solving for x?(1 point)
Responses

15.44876
15.44876

−2.252
negative 2.252

15.038
15.038

12.452

Solve for x in the equation −6.29(x+7.85)=−19.499

Bags of clementines have 12 each. For a party, Sal, Trisha, and Joe each brought bags of clementines. Altogether, there were 180 clementines. Sal brought 4 bags and Joe brought 6. Write the equation to determine how many bags Trisha brought, t.

Dahlia bought Granny Smith and Macintosh apples at the grocery store. The Granny Smith apples were $1.35 each if you bought 6. Find the cost of each Macintosh apple if the total cost is $15 and she bought 6 of each.(1 point)
Each Macintosh apple cost $

Patrick purchased some supplies for his guitar students. He bought 25 guitar picks and 25 guitar strings since they only cost $1 more than the guitar picks. He spent a total of $40. If c is the cost of one guitar pick, find the cost of one guitar string.

Marbles come in two sizes: 1-inch diameter and 2-inch diameter. The 1-inch diameter marbles cost 30 cents less than the 2-inch marbles. Rochelle buys 25 1-inch marbles for her science project and spends exactly $10. Find the cost of a 2-inch marble

A local dumpling shop sold 85,248 dumplings last year. Each plate of dumplings sells for $9.89, and there are 12 dumplings per plate. Which value best estimates the shop’s total earnings from selling dumplings?(1 point)
Responses

8,000,000
8,000,000

800,000
800,000

80,000
80,000

8,000

ANSWER ALL QUESTIONS WITH EXPLANATION

Answer 1

1. The first step in solving the equation 20 = 6x - 4 for x is to add 4 to both sides. This is done to isolate the term containing x on one side of the equation.

2. Shawnece is multiplying both sides of the equation x/7 - 4 = -6 by 7 in order to undo the division of x by 7 in the original problem. By multiplying both sides by 7, the x/7 term will be eliminated and allow for further simplification.

3. Tillie is solving the equation 12 - x = -8. The first step she takes is to subtract 8 from both sides. This is done to isolate the term containing x on one side of the equation.

4. The first step in solving the equation 12(x + 7) = 0 for x is to divide both sides by 12. This is done to isolate the expression (x + 7) on one side of the equation, allowing for further simplification.

5. To solve the equation 0.24(x - 10.2) = 6 for x, divide both sides by 0.24. This will cancel out the coefficient of x and allow for solving for x.

6. To solve for x in the equation 8/11(x+4/5)=24/55, multiply both sides by the reciprocal of 8/11 (which is 11/8). This will cancel out the fraction coefficient and allow for solving for x.

7. In the equation 1.26(x - 7.352) = 6.426, divide both sides by 1.26 to isolate the term containing x. This will cancel out the coefficient and allow for solving for x.

8. In the equation -6.29(x + 7.85) = -19.499, divide both sides by -6.29 to isolate the term containing x. This will cancel out the coefficient and allow for solving for x.

9. The equation to determine how many bags Trisha brought, t, is 4 + 6 + t = 180. This equation represents the sum of the number of bags brought by Sal, Trisha, and Joe being equal to the total number of clementines.

10. The cost of each Macintosh apple can be found by setting up the equation 1.35(6) + x(6) = 15, where x represents the cost of each Macintosh apple. The left side of the equation represents the total cost of the Granny Smith and Macintosh apples, and the right side represents the total cost Dahlia spent. By solving for x, you can find the cost of each Macintosh apple.

11. The cost of one guitar string can be found by setting up the equation 25c + (25c + 1) = 40, where c represents the cost of one guitar pick. The left side of the equation represents the total cost of the guitar picks and guitar strings, and the right side represents the total amount Patrick spent. By solving for (25c + 1), you can find the cost of one guitar string.

12. The cost of a 2-inch marble can be found by setting up the equation 25(1-inch marble) + 30 = 10. The left side of the equation represents the total cost of the 1-inch marbles and the extra 30 cents per marble compared to the 2-inch marbles, and the right side represents the total cost spent by Rochelle. By solving for the 1-inch marble cost, you can find the cost of a 2-inch marble.

13. To estimate the shop's total earnings from selling dumplings, multiply the number of dumplings sold (85,248) by the price per plate ($9.89) and divide by the number of dumplings per plate (12). This calculation gives an estimate of the total earnings from selling dumplings.