2 times a number equals that number plus 5
2 times a number equals that number plus 5 The phrase [I]a number[/I] means an arbitrary variable, let's call it x. 2 times a number means we multiply 2 by x: 2x That number plus 5 means we add 5 to the number x x + 5 The phrase [I]equals[/I] means we set both expressions equal to each other [B]2x = x + 5[/B] <-- This is our algebraic expression If you want to take this further and solve this equation for x, [URL='https://www.mathcelebrity.com/1unk.php?num=2x%3Dx%2B5&pl=Solve']type this expression in the search engine[/URL] and we get: [B]x = 5[/B]
6 times the reciprocal of a number equals 2 times the reciprocal of 7. What is the number We've got two algebraic expressions here. Let's take it in parts: Term 1: The phrase [I]a number[/I] means an arbitrary variable, let's call it x. The reciprocal is 1/x Multiply this by 6: 6/x Term 2: Reciprocal of 7: 1/7 2 times this: 2/7 We set these terms equal to each other: 6/x = 2/7 [URL='https://www.mathcelebrity.com/prop.php?num1=6&num2=2&den1=x&den2=7&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into the search engine[/URL], and we get: [B]x = 21[/B]
76 subtracted from p is equal to the total of g and 227 We've got two algebraic expressions. Take them in pieces: Part 1: 76 subtracted from p We subtract 76 from the variable p p - 76 Part 2: The total of g and 227 The total means a sum, so we add 227 to g g + 227 Now the last piece, the phrase [I]is equal to[/I] means an equation. So we set both algebraic expressions equal to each other: [B]p - 76 = g + 227[/B]
9 divided by the sum of x and 4 is equal to 6 divided by x minus 4. Build our two algebraic expressions first: 9 divided by the sum of x and 4 9/(x + 4) 6 divided by x minus 4 6/(x - 4) The phrase [I]is equal to[/I] means and equation, so we set the algebraic expressions equal to each other: [B]9/(x + 4) = 6/(x - 4) <-- This is our algebraic expression[/B] [B][/B] If the problem asks you to solve for x, we cross multiply: 9(x - 4) = 6(x + 4) To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=9%28x-4%29%3D6%28x%2B4%29&pl=Solve']type this equation into our search engine[/URL] and we get: x = [B]20[/B]
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Squaring a number equals 5 times that number. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. Squaring this number: x^2 5 times this number means we multiply by 5: 5x The phrase [I]equals[/I] means we set both expressions equal to each other: [B]x^2 = 5x [/B] <-- This is our algebraic expression If you want to solve for x, then we subtract 5x from each side: x^2 - 5x = 5x - 5x Cancel the 5x on the right side, leaving us with 0: x^2 - 5x = 0 Factor out x: x(x - 5) So we get x = 0 or [B]x = 5[/B]
sum of 5 times h and twice g is equal to 23 Take this [U]algebraic expressions[/U] problem in pieces. Step 1: 5 times h: 5h Step 2: Twice g means we multiply g by 2: 2g Step 3: sum of 5 times h and twice g means we add 2g to 5h 5h + 2g Step 4: The phrase [I]is equal to[/I] means an equation, so we set 5h + 2g equal to 23: [B]5h + 2g = 23[/B]
twice the difference of a number and 3 is equal to 3 times the sum of a number and 2. We've got 2 algebraic expressions here. Let's take them in parts. Left side algebraic expression: twice the difference of a number and 3 [LIST] [*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x. [*]The word [I]difference[/I] means we subtract 3 from the variable x [*]x - 3 [*]Twice this difference means we multiply (x - 3) by 2 [*]2(x - 3) [/LIST] Right side algebraic expression: 3 times the sum of a number and 2 [LIST] [*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x. [*]The word [I]sum[/I] means we add 2 to the variable x [*]x + 2 [*]3 times the sum means we multiply (x + 2) by 3 [*]3(x + 2) [/LIST] Now, we have both algebraic expressions, the problem says [I]is equal to[/I] This means we have an equation, where we set the left side algebraic expression equal to the right side algebraic expression using the equal sign (=) to get our answer [B]2(x - 3) = 3(x + 2)[/B]
twice the difference of a number and 55 is equal to 3 times the sum of a number and 8 Take this algebraic expression in pieces. Left side: The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x The difference of this number and 55 means we subtract 55 from x x - 55 Twice the difference means we multiply x - 55 by 2 2(x - 55) Right side: The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x The sum of a number and 8 means we add 8 to x x + 8 3 times the sum means we multiply x + 8 by 3 3(x + 8) Now that we have the left and right side of the expressions, we see the phrase [I]is equal to[/I]. This means an equation, so we set the left side equal to the right side: [B]2(x - 55) = 3(x + 8)[/B]
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