A number is added to 7 and the result is multiplied by 4. The final answer is twice the original number . Find the original number.
(x+7)(4) = 2x
that should get you started...
×3,5+3
Let's assume the original number is represented by 'x'.
According to the given information:
Step 1: A number is added to 7: x + 7
Step 2: The result is multiplied by 4: 4(x + 7)
Step 3: The final answer is twice the original number: 2x
Setting up the equation:
4(x + 7) = 2x
Expanding the equation:
4x + 28 = 2x
Moving all variables to one side:
4x - 2x = -28
Combining like terms:
2x = -28
Dividing both sides by 2:
x = -28/2
Simplifying:
x = -14
Therefore, the original number is -14.
To find the original number, let's break down the problem step by step.
Step 1: A number is added to 7.
Let's call the original number "x".
The expression for this step can be written as x + 7.
Step 2: The result from step 1 is multiplied by 4.
The expression for this step can be written as 4(x + 7).
Step 3: The final answer is twice the original number.
The expression for this step can be written as 2x.
Putting it all together, we can write the equation:
4(x + 7) = 2x
Now, let's solve the equation to find the value of x:
1. Distribute the 4 to the terms inside the parentheses:
4x + 28 = 2x
2. Subtract 2x from both sides of the equation to isolate the x term:
4x - 2x + 28 = 2x - 2x
2x + 28 = 0
3. Subtract 28 from both sides to isolate the x term:
2x + 28 - 28 = 0 - 28
2x = -28
4. Divide both sides by 2 to solve for x:
(2x) / 2 = -28 / 2
x = -14
Therefore, the original number is -14.