Find x: how to solve for x in equations, angles and triangles

1. Subtract 7 from both sides.
   $$3x = 15$$
2. Divide by 3.
   $$x = 5$$
3. Check: $3(5) + 7 = 22$ ✓.

Answer: $x = 5$

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1. Angles on a straight line add up to 180°.
   $$x + 2x + 30 = 180$$
2. Collect and solve.
   $$3x = 150 \Rightarrow x = 50$$
3. Check: $50 + 100 + 30 = 180$ ✓.

Answer: $x = 50°$

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1. The angles of a triangle add up to 180°.
   $$x + 2x + 3x = 180$$
2. Solve.
   $$6x = 180 \Rightarrow x = 30$$
3. So the angles are 30°, 60° and 90° — a right triangle.

Answer: $x = 30°$

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1. Pythagoras: the square of the hypotenuse equals the sum of the squares of the legs.
   $$x^2 = 6^2 + 8^2 = 100$$
2. Take the square root. A length is positive, so ignore $-10$.
   $$x = 10$$

Answer: $x = 10$

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1. Matching sides are in the same ratio.
   $$\frac{x}{4} = \frac{9}{6}$$
2. Multiply both sides by 4.
   $$x = \frac{36}{6} = 6$$

Answer: $x = 6$

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