Solving equations and inequalities：練習問題

Solve the following linear equation for \(y\):
\(5y - 7 = 18\)

Solve the following simultaneous equations to find the value of \(x\) and \(y\):
\(5x + 3y = 21\)
\(4x - 3y = 6\)

Find the set of integer values for \(x\) that satisfy the double inequality:
\(2 < 3x - 1 \le 14\)

Find the largest integer value of \(n\) that satisfies the inequality:
\(2n + 5 < 16\)

Solve the linear equation for \(a\):
\(7a - 3 = 3a + 17\)

Solve the inequality:
\( 4x - 7 > 13 \)
Represent your answer using inequality notation.

Solve the inequality \(3(x + 4) < 21\) and represent your answer using inequality notation.

Solve the following equation for \(x\):
\(5x - 12 = 18\)

Part a: Solve the inequality:
\(7n - 5 < 16\)

Part b: Write down the largest integer value of \(n\) that satisfies the inequality from part (a).

Part c: Solve the equation for \(z\):
\(\frac{z}{3} + 4 = 10\)

A rectangle has a length of \(2x + 3\) cm and a width of \(x - 1\) cm.

(a) The perimeter of the rectangle is 28 cm. Form an equation in terms of \(x\) and solve it to find the value of \(x\).
(b) Using your value of \(x\) from part (a), calculate the area of the rectangle.
(c) Solve the inequality \(5y - 4 < 3y + 10\) and show the solution on a number line.