Corinne's solution is incorrect.
To solve the equation 5x = 95, first, you need to isolate x.
Divide both sides of the equation by 5 to get:
5x ÷ 5 = 95 ÷ 5
x = 19
Therefore, the correct solution is x = 19.
Corinne solved the equation below:
5x = 95
5x − 5 = 95 − 5
x = 90
Is Corinne's solution correct? If the solution is incorrect, explain why it is incorrect and show the correct steps to solve the equation. (5 points)
9 answers
An equation is shown below:
4(2x - 5) + 15 = 11
Write the steps you will use to solve the equation and explain each step. (5 points)
4(2x - 5) + 15 = 11
Write the steps you will use to solve the equation and explain each step. (5 points)
To solve the equation 4(2x - 5) + 15 = 11, follow these steps:
Step 1: Distribute the 4 on the left side of the equation:
4(2x - 5) + 15 = 11
8x - 20 + 15 = 11
Step 2: Combine like terms on the left side:
8x - 5 = 11
Step 3: Move the constant term to the right side by subtracting 5 from both sides:
8x = 11 + 5
8x = 16
Step 4: Finally, divide both sides by 8 to solve for x:
x = 16 / 8
x = 2
Therefore, the solution to the equation 4(2x - 5) + 15 = 11 is x = 2.
Step 1: Distribute the 4 on the left side of the equation:
4(2x - 5) + 15 = 11
8x - 20 + 15 = 11
Step 2: Combine like terms on the left side:
8x - 5 = 11
Step 3: Move the constant term to the right side by subtracting 5 from both sides:
8x = 11 + 5
8x = 16
Step 4: Finally, divide both sides by 8 to solve for x:
x = 16 / 8
x = 2
Therefore, the solution to the equation 4(2x - 5) + 15 = 11 is x = 2.
What is the value of z in the equation 3z + 5 = 4z − 8? (4 points)
−13
−1
1
13
−13
−1
1
13
To solve the equation 3z + 5 = 4z - 8, follow these steps:
Step 1: Subtract 3z from both sides of the equation to isolate z variable:
3z + 5 = 4z - 8
3z - 3z + 5 = 4z - 3z - 8
5 = z - 8
Step 2: Add 8 to both sides to get z by itself:
5 + 8 = z - 8 + 8
13 = z
Therefore, the value of z in the equation 3z + 5 = 4z - 8 is z = 13.
So, the correct answer is 13.
Step 1: Subtract 3z from both sides of the equation to isolate z variable:
3z + 5 = 4z - 8
3z - 3z + 5 = 4z - 3z - 8
5 = z - 8
Step 2: Add 8 to both sides to get z by itself:
5 + 8 = z - 8 + 8
13 = z
Therefore, the value of z in the equation 3z + 5 = 4z - 8 is z = 13.
So, the correct answer is 13.
Which of these is a simplified form of the equation 7z + 2 = 8 + 2z + 1z? (4 points)
10z = 6
10z = 10
4z = 6
4z = 10
10z = 6
10z = 10
4z = 6
4z = 10
To simplify the equation 7z + 2 = 8 + 2z + 1z, first, combine like terms on both sides:
7z + 2 = 8 + 2z + 1z
7z + 2 = 8 + 3z
Next, combine the z terms:
7z - 3z = 8 - 2
4z = 6
Therefore, the simplified form of the equation is 4z = 6.
So, the correct option is:
4z = 6
7z + 2 = 8 + 2z + 1z
7z + 2 = 8 + 3z
Next, combine the z terms:
7z - 3z = 8 - 2
4z = 6
Therefore, the simplified form of the equation is 4z = 6.
So, the correct option is:
4z = 6
What is the value of p in the equation 4p + 3(p + 4) = 12p + 12? (4 points)
12
1
0
−1
12
1
0
−1
To solve the equation 4p + 3(p + 4) = 12p + 12, you need to simplify both sides of the equation by applying the distributive property first.
Start by distributing the 3 on the left side:
4p + 3(p + 4) = 12p + 12
4p + 3p + 12 = 12p + 12
Combine like terms:
4p + 3p + 12 = 12p + 12
7p + 12 = 12p + 12
Now, isolate p by moving all terms with p to one side:
7p + 12 = 12p + 12
7p - 12p = 12 - 12
-5p = 0
p = 0
Therefore, the value of p in the equation 4p + 3(p + 4) = 12p + 12 is p = 0.
So, the correct answer is:
0
Start by distributing the 3 on the left side:
4p + 3(p + 4) = 12p + 12
4p + 3p + 12 = 12p + 12
Combine like terms:
4p + 3p + 12 = 12p + 12
7p + 12 = 12p + 12
Now, isolate p by moving all terms with p to one side:
7p + 12 = 12p + 12
7p - 12p = 12 - 12
-5p = 0
p = 0
Therefore, the value of p in the equation 4p + 3(p + 4) = 12p + 12 is p = 0.
So, the correct answer is:
0