Question
upstudy study bank question image url

Solve by using the multiplication principle. \( 4 x=60 \) Choose the correct definition of the multiplication principle. A. \( b=c \) is equivalent to \( b \cdot c=a \). B. \( a=b \) is equivalent to \( b \cdot a=c \). C. \( b=c \) is equivalent to \( a \cdot c=b \cdot c \). D. \( a=b \) is equivalent to \( a \cdot c=b \cdot c \).

Ask by Bates Murray. in the United States
Feb 26,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The multiplication principle states that if \( a = b \), then \( a \cdot c = b \cdot c \). Using this, solving \( 4x = 60 \) gives \( x = 15 \).

Solution

The multiplication principle (or multiplication property of equality) states that if a = b, then for any number c, a·c = b·c. This is exactly what option D states. Now, using this principle to solve 4x = 60: 1. Start with the equation: 4x = 60. 2. To isolate x, divide both sides by 4 (which is multiplying both sides by 1/4, an example of the multiplication principle). Thus,   x = 60/4. 3. Simplify: x = 15. So, x = 15 and the correct definition of the multiplication principle is option D: a = b is equivalent to a·c = b·c.

Answered by UpStudy AI and reviewed by a Professional Tutor

error msg
Explain
Simplify this solution

Mind Expander

To solve the equation \( 4x = 60 \) using the multiplication principle, you can isolate \( x \) by dividing both sides by 4. Once divided, you'll get \( x = 15 \). Now, regarding the multiplication principle, it states that if you have an equation \( a = b \), you can multiply both sides of the equation by a number \( c \) without changing the equality. Therefore, the correct choice is: D. \( a = b \) is equivalent to \( a \cdot c = b \cdot c \).

Latest Algebra Questions

phrase I. The difference between three times \( x \) and fifteen is greater than or equal to five 2. Five more than sixteen times \( x \) is less than or equal to six 3. Three more than two times \( x \) is less than seven \( \square \) 4. Five less than four times \( x \) is less than or equal to sixteen 5. Six times the sum of \( x \) and twelve is less than fourteen 6. The difference between fifteen and two times \( x \) is greater than five 7. The difference between eleven and four times \( x \) is greater than or equal to three 8. The sum of negative three times \( x \) and five is less than or equal to negative four 9. Fourteen less than five times \( x \) is at most eleven \( \qquad \) 10. Twice the sum of nine and \( x \) is greater than twenty II. Ten less than three times \( x \) is greater than eleven 12. Thirteen plus five times \( x \) is no more than thirty 13. Thirteen more than three times \( x \) is no more than the opposite of eleven 14. Half of the sum of \( x \) and six is no less than twenty 15. The difference between negative five times \( x \) and eight is greater than twelve. Solve only your inequalities! Look for your answer at the bottom. \[ \begin{array}{ll} N \quad 2 x+3 \leq 7 & E \\ C & 14-5 x \leq 11 \\ \text { C } 15-2 x>5 & \text { R } \\ F(9+x)>20 \\ E \quad 1 / 2 x+6 x \leq 30 & \text { D } \end{array} 6(x+12)<141 \] \[ \text { L } 5 x-14 \leq 11 \quad H \quad-3 x-5<-4 \] \[ \text { U } 3 x-15 \geq 5 \quad \text { A } 1 / 2(x+6) \geq 20 \] \[ E \quad 6(x-12)>14 \backslash \text { H } \quad 11-4 x \geq 3 \] \[ 3 x-10>11 \quad 0 \quad-5 x-8>12 \] \[ \vee 16 x+5<6 \quad \& \quad 3 x+13 \leq-11 \] \[ \text { Y } 4 x-5 \geq 16 \quad \text { \& } 16 x+5 \leq 6 \]
Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy