If 2(x -1) = 14, then x =?
To solve the equation 2(x – 1) = 14 for x, first distribute the 2 on the left side of the equation:
2x – 2 = 14.
Next, isolate x by adding 2 to both sides of the equation:
2x – 2 + 2 = 14 + 2, 2x = 16.
Finally, divide both sides by 2 to find the value of x:
2x/2 = 16/2, x = 8.
So, x is equal to 8.
Solving Equations with Distribution
Many algebraic equations involve distribute terms like 2(x – 1) where a coefficient multiplies a binomial expression in parentheses. To solve equations containing distribute terms, we first need to apply the distributive property.
The distributive property states that multiplying a coefficient outside a parenthesis with the expression inside is the same as multiplying the coefficient individually with each part inside the parenthesis.
For example:
2(x – 1) is equal to: 2x – 2
To write it as a distributive property equation:
2(x – 1) = 2x – 2
Where the 2 is distributed and multiplied by both the x and -1.
Applying Distribution to Equations
To solve an equation with a distributed term, we first distribute the coefficient inside the parentheses:
2(x – 1) = 14 2x – 2 = 14
Then we can solve the equation as normal by adding 2 to both sides:
2x – 2 + 2 = 14 + 2 2x = 16
And then dividing both sides by 2:
2x/2 = 16/2 x = 8
Therefore, the value of x that makes the original equation true is 8.
Checking the Solution
We can double check that x = 8 is the solution by substituting it back into the original equation:
2(x – 1) = 14 2(8 – 1) = 14 2(7) = 14 14 = 14 ✅
The two sides are equal, so x = 8 checks out as the solution.
Summary
When solving equations with distribute terms like 2(x – 1), we have to apply the distributive property first to remove the parentheses before combining like terms. Once the equation is simplified, we can use addition/subtraction and multiplication/division to isolate the variable and solve for it. Checking the solution by substituting back into the original equation is always a good idea to confirm the accuracy.
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