Math Review of Equivalent Sentences

Math Review of Equivalent Sentences

Math Review of Equivalent Sentences 150 150 Deborah

 

Overview:

Solving equations in algebra depends on using equivalent sentences until the solution is found.  Sentences are equivalent if they have the same solution.  For example, sentences such as x +3 = 8 and 2x = 10 are equivalent because in both of them x = 5.

How to Use Equivalent Sentences

When solving equations, each sentence is equivalent.  Suppose you have the equation x +3 = 8.  In the next step, subtract -3 from both sides of the sentence to have the equivalent sentence x +3-3 = 8-3.  That means that x = 8-3, or x = 5.  The solution to the problem, x=5, is equivalent to the original sentence, x +3 = 8.

Checking for Errors

By using equivalent sentences, students can often pinpoint exactly where they went wrong in attempts to solve an equation.  For  example, suppose the original equation was -6 = y-9.  In the next step, -6 + 9 = y-9 + 9, which gives the equivalent sentence -6 + 9 = y.  The correct answer is 3 = y.  It checks in the original equation, as -6 = 3-9.  Suppose that in the second step, a student subtracted the 9 instead of adding the 9 to the -6, to get the solution y =-15.  The -15 is not correct in the original equation, as -6 is not equal to ( ≠ ) -15 – 9.

When Sentences Are Not Equivalent

Very often, it is a matter of knowing what sentence cannot be an equivalent solution, because it is not equivalent to the others.  In the previous paragraph, x = -15 is not equivalent to the original sentence, -6 = y – 9.  Similarly, if x + 3 = 8 and 2x = 10, the equation x -0.4 = 4.96 does not have an equivalent solution, because x -0.4 +0.4 = 4.96 + 0.4 or x = 5.36.  The variable x is not equivalent in all three equations if it equals 5 in two of them and 5.36 in one of them.

Equivalent Formulas

Students often use formulas to find a solution to an application problem in math.  For example, the formula for the area of a rectangle is A = lw, where l is the length and w is the width.  Sometimes, one might need to solve the equation for one of the variables instead.  When solving for w, the equivalent formula is A/l = w, and when solving for l the equivalent formula is A/w = l.

Interested in pre-algebra tutoring services? Learn more about how we are assisting thousands of students each academic year.

SchoolTutoring Academyis the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Natchez, MS visit: Tutoring in Natchez, MS