4(x-2)=3(1.5+x)
Use Dis.Property
Combine like terms
Solve using inverse operations
I just don't understand!Please explain
4x-8=4.5+3x
4x-3x=4.5+8
x= ....
4 (x - 2) = 3 (1.5 + x)
1) 4x - 8 = 4.5 + 3x Multiply the number outside the par. by the numbers inside the paranthesis. Distributive Property
2) 4x = 12.5 + 3x Eliminate the (-8) from both sided by adding 8 to both sides. Combine like terms and inverse operations.
3) x = 12.5 Get x on one side by subtacting 3x from both sides. Combine like terms and inverse operations.
4) The check is up to you. The answer is x = 12.5.
Sure! Let's break down the steps to solve the given equation using the distributive property, combining like terms, and inverse operations.
Step 1: Distributive Property
First, we apply the distributive property to expand the equation. The distributive property states that for any real numbers a, b, and c: a(b + c) = ab + ac.
So, let's distribute 4 to (x - 2):
4(x - 2) = 4 * x - 4 * 2
4x - 8
And distribute 3 to (1.5 + x):
3(1.5 + x) = 3 * 1.5 + 3 * x
4.5 + 3x
Now, our equation becomes:
4x - 8 = 4.5 + 3x
Step 2: Combining Like Terms
Next, we need to combine the like terms on both sides of the equation. Like terms are the terms that have the same variable and exponent.
On the left side, we have 4x.
On the right side, we have 4.5 and 3x.
To combine these terms, let's move the 3x term to the left side by subtracting 3x from both sides:
4x - 3x - 8 = 4.5 + 3x - 3x
x - 8 = 4.5
Step 3: Solve using Inverse Operations
Lastly, we need to isolate the variable x. To do this, we'll perform inverse operations.
To cancel out the -8 on the left side, we add 8 to both sides:
x - 8 + 8 = 4.5 + 8
x = 12.5
Therefore, the solution to the given equation is x = 12.5.
Remember, it's important to apply these steps systematically to solve equations.