This expression involves these two operations _______ and ___________ .
We will use the _________ to simplify this expression.
The simplified expression looks like _________
This expression involves these two operations addition and multiplication.
We will use the distributive property to simplify this expression.
The simplified expression looks like a + bx.
Simplify: −4(2x+5)
To simplify −4(2x+5), we need to use the distributive property.
The distributive property states that when we multiply a number by a sum, we can distribute the multiplication to each term inside the parentheses.
So, in this case, we multiply -4 by each term inside the parentheses:
-4(2x) = -8x
-4(5) = -20
Therefore, the simplified expression is -8x - 20.
Put the steps in order for solving the equation: −2(4x+8)+2x = −5x+10
Step 1: Distribute -2 to the terms inside the parentheses
Step 2: Combine like terms on both sides of the equation
Step 3: Move all the variables to one side of the equation and the constants to the other side
Step 4: Simplify the equation by combining like terms
Step 5: Divide both sides of the equation by the coefficient of the variable to solve for x
Here is the correct order of steps for solving the equation:
1. −2(4x+8)+2x = −5x+10
2. −8x - 16 + 2x = −5x + 10
3. -6x - 16 = -5x + 10
4. -6x + 5x = 10 + 16
5. -x = 26
6. x = -26
Question
A student solves the following problem: 2(x - 2) + 5x = 24
Step 1: 2x - 4 + 5x = 24
Step 2: 10x - 4 = 24
Step 3: 10x - 4 + 4 = 24 + 4
Step 4: 10x = 28
Step 5: 10x/10=28/10
Step 6: x = 2.8
Where is the mistake? What did the student do incorrectly?
The mistake made by the student is in Step 3.
In step 3, the student adds 4 to only one side of the equation, which is not allowed in algebra.
The correct step should be to add 4 to both sides of the equation:
10x - 4 + 4 = 24 + 4
Now the equation becomes:
10x = 28
Then proceeding with Step 5 and Step 6, the correct solution is x = 2.8.