SOLVING EQUATIONS INVOLVING SIGNED NUMBERS OBJECTIVES. Upon completing this section you should be able to solve equations involving signed numbers. Example 1 Solve for x and check: x + 5 = 3. Solution. Using the same procedures learned in chapter 2, we subtract 5 from each side of the equation obtaining. Example 2 Solve for x and check: - 3x
As you may have seen from other replies, for solving such problems you have to divide the equation into "regimes", based on the expression (s) of x that are enclosed in absolute value brackets. Based on your equation, we have three regimes: (i) x >= 1 (ii) 1/2 2x - 1, giving x < 0. Addition Property of Equality. For all real numbers a, b, and c: If a =b a = b, then a+c= b+c a + c = b + c. If two expressions are equal to each other, and you add the same value to both sides of the equation, the equation will remain equal. The next video shows how to use the addition property of equality to solve equations with fractions. Let's say we have the equation 7 times x is equal to 14. Now before even trying to solve this equation, what I want to do is think a little bit about what this actually means. 7x equals 14, this is the exact same thing as saying 7 times x -- let me write it this way -- 7 times x -- we'll do the x in orange again -- 7 times x is equal to 14. To solve for x , we must first isolate the exponential part. To do this, divide both sides by 5 as shown below. We do not multiply the 5 and the 2 as this goes against the order of operations! 5 ⋅ 2 x = 240 2 x = 48. Now, we can solve for x by converting the equation to logarithmic form. 2 x = 48 is equivalent to log 2 ( 48) = x .
Here is a general method for solving equations by graphing. Step 1 : Let y be equal to the expressions on both sides of the equal sign. Step 2 : Graph the two functions that were created. Step 3 : Approximate the point (s) at which the graphs of the functions intersect. The x coordinate of the point (s) where the graphs of the functions
Solving an Equation with More Than One Solution. In your higher classes, you will learn to solve equations with two or more solutions. Let us take an example of a simple equation. Example: (x – 2) (x – 5) = 0. In this case, the variable x will have two solutions. X – 2 = 0. X = 2. And. X – 5 = 0. X = 5. Thus, the two solutions are x = 2
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    • can you solve an equation