Is the equation true, false, or open? 5x – 10 = 12x + 3
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To determine if the equation is true, false, or open, we need to solve it.
5x - 10 = 12x + 3
First, let's combine like terms by subtracting 5x from both sides:
-10 = 7x + 3
Next, let's isolate x by subtracting 3 from both sides:
-13 = 7x
Now, let's solve for x by dividing both sides by 7:
x = -13/7
Since we have found a value for x, the equation is not open.
Therefore, the equation is true.
To determine if the equation is true, false, or open, we need to solve it step-by-step.
Given equation: 5x - 10 = 12x + 3
Step 1: Simplify the equation.
Start by rearranging the terms to isolate the variable on one side of the equation. Let's move the 12x term to the left side and the -10 and 3 terms to the right side.
5x - 12x = 3 + 10
-7x = 13
Step 2: Solve for x.
Divide both sides of the equation by -7 to isolate the variable x.
-7x/-7 = 13/-7
x = -13/7
Step 3: Check the solution.
Substitute the value of x obtained back into the original equation and simplify.
5(-13/7) - 10 = 12(-13/7) + 3
-65/7 - 10 = -156/7 + 3
(-65 - 70)/7 = (-156 + 21)/7
-135/7 = -135/7
Since both sides of the equation are equal, the equation is true.
Therefore, the equation 5x - 10 = 12x + 3 is true.
To determine if the equation 5x – 10 = 12x + 3 is true, false, or open, we need to follow these steps:
Step 1: Isolate variables on one side of the equation.
5x - 12x = 3 + 10
-7x = 13
Step 2: Simplify the equation further by dividing both sides by the coefficient of x.
-7x / -7 = 13 / -7
x = -13/7
Step 3: Substitute the value of x back into the original equation to check if it holds true.
5(-13/7) - 10 = 12(-13/7) + 3
-65/7 - 10 = -156/7 + 3
-65/7 - 70/7 = -156/7 + 21/7
-135/7 = -135/7
Since both sides of the equation are equal (-135/7 = -135/7), the equation 5x – 10 = 12x + 3 is true.