Final answer:
To solve the algebraic equations, we perform operations to isolate the variable on one side, using addition, subtraction, multiplication, or division as needed. We found the values of d, c, p, and q by manipulating the equations step by step.
Step-by-step explanation:
To solve each equation for the given variable, we need to isolate the variable on one side of the equation. Here's how we can solve each one:
Solve for d:
7/6 d + 4/3 = -1/3
Step 1: Subtract 4/3 from both sides to isolate the term with d.
7/6 d = -1/3 - 4/3
7/6 d = -5/3
Step 2: Multiply both sides by the reciprocal of 7/6 to solve for d.
d = (-5/3) × (6/7)
d = -10/7 or -1 3/7
Solve for c:
5/9 c - 2/3 = 7/9
Step 1: Add 2/3 to both sides to isolate the term with c.
5/9 c = 7/9 + 2/3
5/9 c = 7/9 + 6/9
5/9 c = 13/9
Step 2: Multiply both sides by the reciprocal of 5/9 to solve for c.
c = (13/9) × (9/5)
c = 13/5 or 2 3/5
Solve for p:
7/9 p + 8/3 = -p
Step 1: Add p to both sides and subtract 8/3 from both sides.
7/9 p + p = -8/3
16/9 p = -8/3
Step 2: Multiply both sides by the reciprocal of 16/9 to solve for p.
p = (-8/3) × (9/16)
p = -3/2 or -1 1/2
Solve for q:
2/7 = 4/5 + 9q
Step 1: Subtract 4/5 from both sides to isolate the term with q.
9q = 2/7 - 4/5
9q = 10/35 - 28/35
9q = -18/35
Step 2: Divide both sides by 9 to solve for q.
q = (-18/35) / 9
q = -18/35 × 1/9
q = -2/35