A linear equation is termed using the linear equation method. There are number of ways to achieve the solution of given equation (2x+2)/4 = (x-3)/3. A linear equation, for example, could be written in standard form, slope-intercept formation, or point-slope form. However that we have learned how this equation is states, let’s look at its standard form.
We can watch that it fluctuates depends on the number of variables, and it is significant to keep in mind that all of the variations in the equation should have a degree of 1 as their maxima (and one) value.
Q. Given Linear Equation:- (2x+2)/4 = (x-3)/3
Solution (2x+2)/4 = (x-3)/3:
One have to isolate the variable x in order which to step-by-step solving the (2x+2)/4 = (x-3)/3 equation. Here is how one can go with it:
Determine a common denominator for every sides of the equation to first get off the fraction values. As 12 is the least common multiple of 4 and 3, it gives as the common denominator in this thing.
- (12 * (2x+2))/4 = (12 * (x-3))/3
Now eliminate the denominators to simplify both sides:
- (3 * (2x+2)) = (4 * (x-3))
Distribute the constants on the equation’s left and right sides:
- 6x + 6 = 4x – 12
Put the constant terms on one side of the equation and the variable terms (those with x) on the other. To determine this, add twelve to each sides and subtract 4x from both sides:
- 6x – 4x = -12 – 6
- 2x = -18
- By dividing both sides by 2, you may finally find x: 2x/2 = -18/2
- x = -9
- As a result, the solution to the equation is x = -9.
To get this more easily lets dive into the steps of this solution (2x+2)/4 = (x-3)/3
Step 1: Do away with fractions
- The initial formula is:
- (2x + 2)/4 = (x – 3)/3
- Finding a common denominator, in this case the least common multiple (LCM) of 4 and 3, which is 12, will allow you to eliminate the fractions.
- To eliminate the fractions, you multiply both sides of the equation by 12.
- 12 * [(2x + 2)/4] = 12 * [(x – 3)/3]’
Step 2: Condense
- You may now make both sides simpler:
- The left side gives you (2x + 2) * 3 since the 4 in the denominator cancels out the 12 in the numerator.
- The 3 in the denominator cancels out with the 12 in the numerator on the right side, leaving (x – 3)*4.
- Thus, the equation is:
- 3(2x + 2) = 4(x – 3)
Third step: Distribute
- Distribute the constants on the equation’s left and right sides:
- 3 * 2x + 3 * 2 = 4 * x – 4 * 3
- That amounts to: 6x + 6 = 4x – 12
Step 4: Set Aside Variable Terms
- We wish to move the constant terms to one side of the equation and the variable terms (those with x) to the other side in order to isolate them. To get this, add on 12 to each sides and minus 4x from both sides:
- 6x – 4x + 6 + 12 = 4x – 4x – 12 + 12
- That amounts to: 2x + 18 = 0
Step 5: Calculate x.
- You now wish to find x’s value. Subtract 18 from both sides of the equation to isolate x on one side:
- 2x + 18 – 18 = 0 – 18
- That amounts to:
- 2x = -18
- Divided by 2 on both sides to determine the value of x.
- (2x)/2 = (-18)/2
- x = -9
Graph (2x+2)/4 = (x-3)/3
Equations with Lines
An linear equation always have the maximum power of the variable is consistently 1. There is another name of this type of linear equation such as a one-degree equation. A linear equation with one variable has the conventional form Axe + B = 0. The variables x and A are variables in this scenario, while B is a constant. A linear equation with two variables has the conventional form Axe + By = C.
A linear equation is defined.
Equations with a maximum degree of 1 are said to be linear. As a result, no variable in a linear equation has an exponent greater than 1. And the Graph representation of this equation form always a straight line.
A linear equating is an algebraic equation in which every term has an exponent of one, and also, when plotted on a graph, always gives a straight line. For this specific approach, it is referred to as a “linear equation”.
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