Arthur writes the equation a=10b−7. He wants to rewrite it in terms of b. In Arthur’s first step, what value should he add to both sides of the equation?(1 point)
Arthur should add 7 to both sides of the equation.
Tilda writes the equation 5y=20x+8. She wants to rewrite the equation in terms of x. After subtracting 8 from both sides of the equation, what number should she divide both sides of the equation by in order to accomplish this goal?(1 point)
Tilda should divide both sides of the equation by 20 in order to rewrite it in terms of x.
A string is cut in two so that one section is 5 inches longer than the other. Twice the length of the longer section is three times the length of the shorter section. Write an equation that allows you to solve for the length of the shorter section. How long is the shorter section?(1 point)
Let's call the length of the shorter section x inches.
According to the problem, the longer section is 5 inches longer than the shorter section, so its length is x + 5 inches.
Twice the length of the longer section is three times the length of the shorter section, so we can write the equation as:
2(x + 5) = 3x
Now, let's solve this equation to find the value of x:
2x + 10 = 3x
10 = 3x - 2x
10 = x
So, the shorter section is 10 inches long.
Andrea is 6 years younger than Tony. In two years, Tony will be three times as old as Andrea. Let a be Tony’s current age. Which of these linear equations can be used to find Andrea’s and Tony’s current ages?
Let's solve this problem step by step:
Let a be Tony's current age. This means Andrea's current age can be represented as a - 6.
In two years, Tony's age will be a + 2, and Andrea's age will be (a - 6) + 2, which simplifies to a - 4.
According to the problem, Tony's age in two years will be three times Andrea's age in two years, so we can write the equation as:
a + 2 = 3(a - 4)
Now, let's simplify this equation:
a + 2 = 3a - 12
2 + 12 = 3a - a
14 = 2a
To find Andrea's current age, substitute the value of a/2 back into the equation a - 6.
(a - 6) - 6 = a - 12
Therefore, the linear equation that can be used to find Andrea's and Tony's current ages is:
a - 12 = 14 - 12
Simplifying this equation, we get:
a - 12 = 2
Therefore, the equation a - 12 = 2 can be used to find Andrea's and Tony's current ages.
Five less than three-fourths of x is seven. If x equals 16, what is the last property of equality you would use to justify the solution to this problem?(1 point)
Manipulate the equation y=7x−12 so that it is written in terms of x. Which equation is equivalent to y=7x−12?(1 point)
To rewrite the equation y = 7x - 12 in terms of x, we need to isolate x on one side of the equation.
Adding 12 to both sides of the equation, we have:
y + 12 = 7x
Now, we divide both sides of the equation by 7 to solve for x:
(y + 12)/7 = x
Therefore, the equivalent equation to y = 7x - 12 in terms of x is:
x = (y + 12)/7.