Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

1. \(3x+3=-14\)
2. \(-4x+7=5\)
3. \(-15x-2=-1\)
4. \(-10x-7=12\)
5. \(-8x-13=-10\)
6. \(13x+3=9\)
7. \(12x-10=-13\)
8. \(8x+8=-11\)
9. \(8x+14=-1\)
10. \(8x+3=8\)
11. \(10x+11=4\)
12. \(7x+8=-7\)

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{+3}& = &-14 \\\Leftrightarrow & 3x \color{red}{+3}\color{blue}{-3} & = &-14\color{blue}{-3} \\\Leftrightarrow &3x & = &-17\\\Leftrightarrow & \color{red}{3}x & = &-17\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-17}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{3} } & & \\ & V = \left\{ \frac{-17}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{+7}& = &5 \\\Leftrightarrow & -4x \color{red}{+7}\color{blue}{-7} & = &5\color{blue}{-7} \\\Leftrightarrow &-4x & = &-2\\\Leftrightarrow & \color{red}{-4}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{-2}& = &-1 \\\Leftrightarrow & -15x \color{red}{-2}\color{blue}{+2} & = &-1\color{blue}{+2} \\\Leftrightarrow &-15x & = &1\\\Leftrightarrow & \color{red}{-15}x & = &1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{15} } & & \\ & V = \left\{ \frac{-1}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{-7}& = &12 \\\Leftrightarrow & -10x \color{red}{-7}\color{blue}{+7} & = &12\color{blue}{+7} \\\Leftrightarrow &-10x & = &19\\\Leftrightarrow & \color{red}{-10}x & = &19\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{19}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{10} } & & \\ & V = \left\{ \frac{-19}{10} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{-13}& = &-10 \\\Leftrightarrow & -8x \color{red}{-13}\color{blue}{+13} & = &-10\color{blue}{+13} \\\Leftrightarrow &-8x & = &3\\\Leftrightarrow & \color{red}{-8}x & = &3\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{3}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{+3}& = &9 \\\Leftrightarrow & 13x \color{red}{+3}\color{blue}{-3} & = &9\color{blue}{-3} \\\Leftrightarrow &13x & = &6\\\Leftrightarrow & \color{red}{13}x & = &6\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{6}{13} \\\Leftrightarrow & \color{green}{ x = \frac{6}{13} } & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{-10}& = &-13 \\\Leftrightarrow & 12x \color{red}{-10}\color{blue}{+10} & = &-13\color{blue}{+10} \\\Leftrightarrow &12x & = &-3\\\Leftrightarrow & \color{red}{12}x & = &-3\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-3}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{+8}& = &-11 \\\Leftrightarrow & 8x \color{red}{+8}\color{blue}{-8} & = &-11\color{blue}{-8} \\\Leftrightarrow &8x & = &-19\\\Leftrightarrow & \color{red}{8}x & = &-19\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-19}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{8} } & & \\ & V = \left\{ \frac{-19}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{+14}& = &-1 \\\Leftrightarrow & 8x \color{red}{+14}\color{blue}{-14} & = &-1\color{blue}{-14} \\\Leftrightarrow &8x & = &-15\\\Leftrightarrow & \color{red}{8}x & = &-15\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-15}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{8} } & & \\ & V = \left\{ \frac{-15}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{+3}& = &8 \\\Leftrightarrow & 8x \color{red}{+3}\color{blue}{-3} & = &8\color{blue}{-3} \\\Leftrightarrow &8x & = &5\\\Leftrightarrow & \color{red}{8}x & = &5\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{5}{8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{+11}& = &4 \\\Leftrightarrow & 10x \color{red}{+11}\color{blue}{-11} & = &4\color{blue}{-11} \\\Leftrightarrow &10x & = &-7\\\Leftrightarrow & \color{red}{10}x & = &-7\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-7}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{10} } & & \\ & V = \left\{ \frac{-7}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{+8}& = &-7 \\\Leftrightarrow & 7x \color{red}{+8}\color{blue}{-8} & = &-7\color{blue}{-8} \\\Leftrightarrow &7x & = &-15\\\Leftrightarrow & \color{red}{7}x & = &-15\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-15}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{7} } & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)