Support each conclusion with a reason.
1. Given: 6x+2=12 Conclusion: 6x=10
2 Given m<1+m<2=90 Conclusion: m<1=90-m<2
3 Given x=m<c. Conclusion: 2x=m<c+x
4 Given q-x=r Conclusion: 4(q-x)=4r
5 given M<q-m<4=90, m<q=4m<r Conclusion: 4m<R-m<r=90
6 Given CD=AF-2CD Conclusion 3cd=af
7 Given 5(y-x)=20 Conclusion 5y-5x=20
8 Given m<aox=2m<xob. Conclusion m<aox=140
1. Given: 6x+2=12
Conclusion: 6x=10
Reason: To isolate the variable 'x', we need to subtract 2 from both sides of the equation. This results in 6x=10.
2. Given: m<1+m<2=90
Conclusion: m<1=90-m<2
Reason: To solve for m<1, we need to subtract m<2 from both sides of the equation. This gives us m<1 = 90 - m<2.
3. Given: x=m<c
Conclusion: 2x=m<c+x
Reason: By multiplying both sides of the equation x=m<c by 2, we obtain 2x = m<c + x.
4. Given: q-x=r
Conclusion: 4(q-x)=4r
Reason: If we multiply both sides of the equation q-x=r by 4, we get 4(q-x) = 4r.
5. Given: M<q-m<4=90, m<q=4m<r
Conclusion: 4m<R-m<r=90
Reason: The given angle relationships indicate that M<q-m<4 is equal to 90 degrees, and m<q is equal to 4m<r. By rearranging the equation, we can conclude that 4m<R-m<r is also equal to 90 degrees.
6. Given: CD=AF-2CD
Conclusion: 3cd=af
Reason: By adding 2CD to both sides of the equation CD=AF-2CD, we can simplify the equation to 3CD = AF. Therefore, the conclusion is 3cd = af.
7. Given: 5(y-x)=20
Conclusion: 5y-5x=20
Reason: By distributing the 5 to both terms within the parentheses, we get 5y - 5x = 20.
8. Given: m<aox=2m<xob
Conclusion: m<aox=140
Reason: Since m<aox is equal to 2m<xob, and 2 multiplied by 70 (the measure of m<xob) is equal to 140, we can conclude that m<aox = 140.
1. Given: 6x + 2 = 12
Conclusion: 6x = 10
Reason: To isolate the variable, subtract 2 from both sides of the equation. This results in 6x = 10.
2. Given: m<1 + m<2 = 90
Conclusion: m<1 = 90 - m<2
Reason: To solve for m<1, subtract m<2 from both sides of the equation. This gives us m<1 = 90 - m<2.
3. Given: x = m<c
Conclusion: 2x = m<c + x
Reason: Multiply both sides of the equation by 2, which gives us 2x = 2(m<c). Then we can rewrite the equation as 2x = m<c + x.
4. Given: q - x = r
Conclusion: 4(q - x) = 4r
Reason: Multiply both sides of the equation by 4, which gives us 4(q - x) = 4r.
5. Given: M<q - m<4 = 90, m<q = 4m<r
Conclusion: 4m < R - m < r = 90
Reason: Combine the two given equations by substituting m<q with 4m<r. This gives us 4m < R - m < r.
6. Given: CD = AF - 2CD
Conclusion: 3CD = AF
Reason: Combine the like terms on the right side of the equation. This results in 3CD = AF.
7. Given: 5(y - x) = 20
Conclusion: 5y - 5x = 20
Reason: Distribute the 5 to both terms within the parentheses on the left side of the equation. This gives us 5y - 5x = 20.
8. Given: m<aox = 2m<xob
Conclusion: m<aox = 140
Reason: Since both angles have the same measure, we can equate them to each other. Therefore, m<aox = 140.