Question

Sarita showed the steps to solving the equation.

5 (x minus 3) + 7 (x + 4) = 73
Steps
Sarita’s Solution
Sarita’s Verification
1
5 x minus 15 + 7 x + 28 = 73
5 (5 minus 3) + 7 (5 + 4) = 73. 5 (negative 2) + 7 (9) = 73. Negative 10 + 63 = 73. 53 not-equal-to 73.
2
(5 + 7) x + (negative 15 + 28) = 73
3
12 x + 13 = 73
4
12 x + 60
5
x = 5

When Sarita tried to verify her answer, she found it was wrong. Which explains her mistake?
Sarita’s solution is correct. She made an error in her verification.
Sarita was supposed to add the 5 and 7 in the first step.
Sarita added +13 instead of Negative 13 in the fourth step.
Sarita was supposed to use the division property of equality in the third step.

Answer 1

Explanation:
The correct answer is option 3: Sarita added +13 instead of Negative 13 in the fourth step.

In step 3, Sarita correctly combined the x terms and the constant terms to get 12x + 13 = 73. However, in step 4, she made a mistake while subtracting 13 from both sides. Instead of subtracting 13, she added 13 to both sides, which resulted in 12x + 60. This mistake led to an incorrect answer, and Sarita's verification showed that 53 was not equal to 73.

Therefore, the mistake in Sarita's solution was in step 4 where she added 13 instead of subtracting it.

Answer 2

Which is the solution to the equation 0.5 x + 4.2 = 5.9? Round to the nearest tenth if necessary.

Answer 3

Subtracting 4.2 from both sides of the equation gives:

0.5x = 1.7

Dividing both sides by 0.5 gives:

x = 3.4

Rounded to the nearest tenth, the solution is x = 3.4.

Answer 4

What is the value of x?

Four-fifths x minus StartFraction 1 Over 10 Endfraction = StartFraction 3 Over 10 EndFraction

Answer 5

First, we can simplify the left side of the equation by combining the fractions:

Four-fifths x - 1/10 = 3/10

Next, we'll isolate the variable term, Four-fifths x, by adding 1/10 to both sides:

Four-fifths x = 3/10 + 1/10

Four-fifths x = 4/10

Simplifying the right side by dividing both sides by 2:

Four-fifths x = 2/5

Finally, we can solve for x by multiplying both sides by the reciprocal of four-fifths, which is five-fourths:

x = (5/4) * (2/5)

x = 1

Therefore, the value of x is 1.

Answer 6

Jeannie works 5 hours on Tuesday, 3 hours on Wednesday, and 4.5 hours on Thursday. If h represents her hourly pay rate, which expression below shows the amount she earned?

Answer 7

Assuming Jeannie earns a consistent hourly pay rate for all three days, her total earnings can be found by multiplying her hours worked by her hourly pay rate and then adding them up:

Total earnings = (hours worked on Tuesday * h) + (hours worked on Wednesday * h) + (hours worked on Thursday * h)

Substituting in the given values:

Total earnings = (5 * h) + (3 * h) + (4.5 * h)

Simplifying:

Total earnings = 12.5h

Therefore, the expression that shows the amount Jeannie earned is 12.5h.

Answer 8

Jubal wrote the four equations below. He examined them, without solving them, to determine which equation has no solution.

7 x + 1 = 7 x+ 1. 3 x + 2 = 3 x minus 2. 4 x + 1 = 3 x + 8. negative 2 x minus 1 = negative 2 x minus 1.

Which of Jubal’s equations has no solution?
7 x + 1 = 7 x+ 1
3 x + 2 = 3 x minus 2
4 x + 1 = 3 x + 8
negative 2 x minus 1 = negative 2 x minus 1

Answer 9

The equation that has no solution is:

3 x + 2 = 3 x minus 2

To see why this equation has no solution, we can simplify it:

3 x + 2 = 3 x - 2

Subtracting 3x from both sides:

2 = -2

This is a contradiction, since 2 cannot equal -2. Therefore, the original equation has no solution.

Answer 10

After getting 5 new rocks, George gave half of his rock collection to Susan. If George gave Susan 36 rocks, which equation could be used to determine how many rocks George started with?

One-half x = 36 + 5
One-half (x minus 5) = 36
One-half (x + 5) = 36
One-half x + 5 = 36