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### High School Mathematics1.19 Linear Equations - One Variable

 An equation is an equality connecting with some unknowns. The unknowns are represented by letters and are called variables. If the equation has only one unknown, it is called an equation with one variable. The word Linear means of degree one. Example: Divide 64 into two parts such that three times the greater part will be equal to five times the smaller one. Solution: Let x be the greater part. Then 64 - x is the smaller part. Then 3x = 5(64 - x) 3x = 320 - 5x 3x + 5x = 320 8x = 320 The two parts are 40 and 24. Example: Find a number such that one-fourth of it is less than one-third of it by 4. Solution: Let the number be x. One-fourth of it is less than one-third of it by 4: x/4 + 4 = x/3 x/4 + 4 = x/3 x/4 + 4 = x/3 (x+16)/4 = x/3 ---- multiplying both sides by 12 we have 12 ((x+16)/4) = 12 (x/3) 3x + 48 = 4x 3x + 48 - 3x = 4x - 3x 48 = x The number is 48. Directions: Solve the following linear equations. Also write at least 10 examples of your own.
 Q 1: Find a number such that one-third of it is less than one-half of it by four. 243026 Q 2: Find a number, if half of which when added to 3, is equal to 12 diminished by 1/4 th of that number. (Hint: Algebraic equation can be written as x/2 + 3 = 12 - x/4 )401210 Q 3: Divide 9 into two parts so that thrice the smaller number is equal to twice the larger number plus 2. Find the numbers. (Hint: Let x be the smaller number. Then the larger number is 9-x. The equation can be written as 3(x) = 2 (9-x) + 2. Find x and 9-x) 4 and 67 and 54 and 5 Q 4: Divide 17 into two parts so that six times the smaller number is equal to five times the larger number plus 3. Find the numbers. 6 and 117 and 108 and 9 Q 5: Divide 25 into two parts so that six times the smaller number is equal to four times the larger number. Find the numbers. 11 and 1410 and 159 and 16 Q 6: Find a number such that one-fourth of it is less than one-third of it by 3. 423336 Q 7: Divide 40 into two parts so that one-third of the greater part may be equal to half of the lesser one.30 and 1020 and 1024 and 16 Q 8: Dad is seven times as old as his son. 10 years later, he will be three times as old as his son. Find their ages.dad is 35 years and son is 7 yearsdad is 35 years and son is 5 yearsdad is 43 years and son is 6 years Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!

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