- Every operation you perform on one side of an equation must be performed on both sides of the equals sign.
1. Solve: 3x = 2x + 1 Solution: 3x - 2x = 1 x = 1 | By subtracting 2x from each side, the variables are all on the same side of the equation. By combining like terms, the variable is isolated, and the equation is simplified and solved. | |
2. Solve: .4x = .2(.6x) - 4 Solution: .4x = .12x - 4 .4x - .12x = -4 .28x = -4 .28x/.28 = -4/.28 x = -100/7 | Following the order of operations, multiplication is done first. By subtracting .12x from each side of the equation, the variables are all on the same side. Combine like terms to simplify. Divide each side by .28 to isolate the variable. Once the variable is all alone, the answer is found (it is converted to a fraction because it made more sense than the decimal answer of -14.28571429 - a calculator was used for the conversion). |
This section will help you understand how to solve this type of equation.
- Fractions are division problems.
- Know how to find an LCM.for an explanation of LCMs.
- Order of Operations
- Multiplicative property of equality:
If a = b, then ac = bc when a, b,
and c are real numbers. 
1. Solve: y 1 y
- + - = -
2 4 6
Solution:
12y 12 12y
--- + -- = ---
2 4 6
6y + 3 = 2y
4y = -3
y = -3/4 | The LCM of the denominators is 12. Multiply each numerator by the LCM. Cancel out the denominators to rid the problem of fractions. The denominators are canceled out. Now, solve for y. By subtracting 2y and 3 from each side, the equation is simplified to something we can easily deal with. By dividing each side by 4, y is isolated and the answer is found. |
This section assumes you know how to factor, and will help you understand quadratic equations.
- Quadratic equations are written in the following form: ax2 + bx + c = d. When d equals zero, the equation is said to be in standard form.
- Zero Factor Theorem:
If pq = 0, then either p or q or
both are equal to 0 if p
and q are real numbers. 1. Solve: x2 - x = 42 Solution: x2 - x - 42 = 0 (x - 7)(x + 6) = 0 x - 7 = 0 x + 6 = 0 x = 7 x = -6 x = 7 or -6 | Write the equation in standard form. Factor the equation. The zero factor theorem says that either one factor or both must equal zero, so we set each factor equal to zero and solve for x. Each factor has its own answer. Since you can only plug one number into the original equation to see if it works, the answer is written with the word or separating the answers. |
This post was written by: Yousuf
who is working hard to post Math material from all over the world on Mathnews.
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