Write equations whose solution is . Share the equations you made with each other and discuss the methods used.

Question

Homi · Accepted Answer

We want to create equations. The unknown value $y$ must be 5.

Step 1 — Creating the equations We will start with $y=5$ . Then we apply operations to both sides. This keeps the equation balanced.

For our first equation, we add 3 to both sides. $y + 3 = 5 + 3$ $y + 3 = 8$ Our first equation is $y+3=8$ .

For our second equation, we multiply by 2. $2 \times y = 2 \times 5$ $2y = 10$ Our second equation is $2y=10$ .

For our third equation, we multiply by 3. $3 \times y = 3 \times 5$ $3y = 15$ Then we subtract 4 from both sides. $3y - 4 = 15 - 4$ $3y - 4 = 11$ Our third equation is $3y-4=11$ .

For our fourth equation, we divide by 2. $\frac{y}{2} = \frac{5}{2}$ $\frac{y}{2} = 2.5$ Then we add 1 to both sides. $\frac{y}{2} + 1 = 2.5 + 1$ $\frac{y}{2} + 1 = 3.5$ Our fourth equation is $\frac{y}{2} + 1 = 3.5$ .

$\boxed{\text{We have created four equations.}}$

Step 2 — Solving the first equation Our first equation is $y+3=8$ . We want to find the value of $y$ . We use the inverse operation of addition. The inverse of adding 3 is subtracting 3. We subtract 3 from both sides. $y + 3 - 3 = 8 - 3$ $y = 5$ The solution for the first equation is 5.

$\boxed{y=5}$

Step 3 — Solving the second equation Our second equation is $2y=10$ . We want to find the value of $y$ . We use the inverse operation of multiplication. The inverse of multiplying by 2 is dividing by 2. We divide both sides by 2. $\frac{2y}{2} = \frac{10}{2}$ $y = 5$ The solution for the second equation is 5.

$\boxed{y=5}$

Step 4 — Solving the third equation Our third equation is $3y-4=11$ . This equation has two operations. First, we deal with the subtraction. We use the inverse operation of subtraction. The inverse of subtracting 4 is adding 4. We add 4 to both sides. $3y - 4 + 4 = 11 + 4$ $3y = 15$ Now, we deal with the multiplication. We use the inverse operation of multiplication. The inverse of multiplying by 3 is dividing by 3. We divide both sides by 3. $\frac{3y}{3} = \frac{15}{3}$ $y = 5$ The solution for the third equation is 5.

$\boxed{y=5}$

Step 5 — Solving the fourth equation Our fourth equation is $\frac{y}{2} + 1 = 3.5$ . This equation also has two operations. First, we deal with the addition. We use the inverse operation of addition. The inverse of adding 1 is subtracting 1. We subtract 1 from both sides. $\frac{y}{2} + 1 - 1 = 3.5 - 1$ $\frac{y}{2} = 2.5$ Now, we deal with the division. We use the inverse operation of division. The inverse of dividing by 2 is multiplying by 2. We multiply both sides by 2. $\frac{y}{2} \times 2 = 2.5 \times 2$ $y = 5$ The solution for the fourth equation is 5.

$\boxed{y=5}$

Answer

(i) An equation whose solution is $y=5$ is $y+3=8$ . (ii) Another equation whose solution is $y=5$ is $2y=10$ . (iii) A third equation whose solution is $y=5$ is $3y-4=11$ . (iv) A fourth equation whose solution is $y=5$ is $\frac{y}{2} + 1 = 3.5$ .

Question 19

Answer

More questions in IT

7.3 Mind the Mistake, Mend the Mistake