Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{-8}& = &-1 \\\Leftrightarrow & -6x \color{red}{-8}\color{blue}{+8} & = &-1\color{blue}{+8} \\\Leftrightarrow &-6x & = &7\\\Leftrightarrow & \color{red}{-6}x & = &7\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{7}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{6} } & & \\ & V = \left\{ \frac{-7}{6} \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{+11}& = &-6 \\\Leftrightarrow & 4x \color{red}{+11}\color{blue}{-11} & = &-6\color{blue}{-11} \\\Leftrightarrow &4x & = &-17\\\Leftrightarrow & \color{red}{4}x & = &-17\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-17}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{4} } & & \\ & V = \left\{ \frac{-17}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{+13}& = &12 \\\Leftrightarrow & -8x \color{red}{+13}\color{blue}{-13} & = &12\color{blue}{-13} \\\Leftrightarrow &-8x & = &-1\\\Leftrightarrow & \color{red}{-8}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-1}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{-12}& = &6 \\\Leftrightarrow & 7x \color{red}{-12}\color{blue}{+12} & = &6\color{blue}{+12} \\\Leftrightarrow &7x & = &18\\\Leftrightarrow & \color{red}{7}x & = &18\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{18}{7} \\\Leftrightarrow & \color{green}{ x = \frac{18}{7} } & & \\ & V = \left\{ \frac{18}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{+7}& = &7 \\\Leftrightarrow & 8x \color{red}{+7}\color{blue}{-7} & = &7\color{blue}{-7} \\\Leftrightarrow &8x & = &0\\\Leftrightarrow & \color{red}{8}x & = &0\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{0}{8} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{+13}& = &-8 \\\Leftrightarrow & 9x \color{red}{+13}\color{blue}{-13} & = &-8\color{blue}{-13} \\\Leftrightarrow &9x & = &-21\\\Leftrightarrow & \color{red}{9}x & = &-21\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-21}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{+14}& = &5 \\\Leftrightarrow & 2x \color{red}{+14}\color{blue}{-14} & = &5\color{blue}{-14} \\\Leftrightarrow &2x & = &-9\\\Leftrightarrow & \color{red}{2}x & = &-9\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-9}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{2} } & & \\ & V = \left\{ \frac{-9}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{-9}& = &3 \\\Leftrightarrow & -7x \color{red}{-9}\color{blue}{+9} & = &3\color{blue}{+9} \\\Leftrightarrow &-7x & = &12\\\Leftrightarrow & \color{red}{-7}x & = &12\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{12}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{7} } & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{+14}& = &-12 \\\Leftrightarrow & 3x \color{red}{+14}\color{blue}{-14} & = &-12\color{blue}{-14} \\\Leftrightarrow &3x & = &-26\\\Leftrightarrow & \color{red}{3}x & = &-26\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-26}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{3} } & & \\ & V = \left\{ \frac{-26}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{-2}& = &13 \\\Leftrightarrow & 4x \color{red}{-2}\color{blue}{+2} & = &13\color{blue}{+2} \\\Leftrightarrow &4x & = &15\\\Leftrightarrow & \color{red}{4}x & = &15\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{15}{4} \\\Leftrightarrow & \color{green}{ x = \frac{15}{4} } & & \\ & V = \left\{ \frac{15}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{-10}& = &2 \\\Leftrightarrow & 13x \color{red}{-10}\color{blue}{+10} & = &2\color{blue}{+10} \\\Leftrightarrow &13x & = &12\\\Leftrightarrow & \color{red}{13}x & = &12\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{12}{13} \\\Leftrightarrow & \color{green}{ x = \frac{12}{13} } & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{+8}& = &-13 \\\Leftrightarrow & -11x \color{red}{+8}\color{blue}{-8} & = &-13\color{blue}{-8} \\\Leftrightarrow &-11x & = &-21\\\Leftrightarrow & \color{red}{-11}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-21}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{21}{11} } & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)