Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{-9}& = &7 \\\Leftrightarrow & 11x \color{red}{-9}\color{blue}{+9} & = &7\color{blue}{+9} \\\Leftrightarrow &11x & = &16\\\Leftrightarrow & \color{red}{11}x & = &16\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{16}{11} \\\Leftrightarrow & \color{green}{ x = \frac{16}{11} } & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{-5}& = &-3 \\\Leftrightarrow & 15x \color{red}{-5}\color{blue}{+5} & = &-3\color{blue}{+5} \\\Leftrightarrow &15x & = &2\\\Leftrightarrow & \color{red}{15}x & = &2\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{2}{15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{15} } & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{+4}& = &-2 \\\Leftrightarrow & 15x \color{red}{+4}\color{blue}{-4} & = &-2\color{blue}{-4} \\\Leftrightarrow &15x & = &-6\\\Leftrightarrow & \color{red}{15}x & = &-6\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-6}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{-5}& = &4 \\\Leftrightarrow & -10x \color{red}{-5}\color{blue}{+5} & = &4\color{blue}{+5} \\\Leftrightarrow &-10x & = &9\\\Leftrightarrow & \color{red}{-10}x & = &9\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{9}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{10} } & & \\ & V = \left\{ \frac{-9}{10} \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{+14}& = &2 \\\Leftrightarrow & -9x \color{red}{+14}\color{blue}{-14} & = &2\color{blue}{-14} \\\Leftrightarrow &-9x & = &-12\\\Leftrightarrow & \color{red}{-9}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-12}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{+4}& = &-13 \\\Leftrightarrow & 3x \color{red}{+4}\color{blue}{-4} & = &-13\color{blue}{-4} \\\Leftrightarrow &3x & = &-17\\\Leftrightarrow & \color{red}{3}x & = &-17\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-17}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{3} } & & \\ & V = \left\{ \frac{-17}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{+9}& = &6 \\\Leftrightarrow & 8x \color{red}{+9}\color{blue}{-9} & = &6\color{blue}{-9} \\\Leftrightarrow &8x & = &-3\\\Leftrightarrow & \color{red}{8}x & = &-3\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-3}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{-10}& = &-6 \\\Leftrightarrow & -6x \color{red}{-10}\color{blue}{+10} & = &-6\color{blue}{+10} \\\Leftrightarrow &-6x & = &4\\\Leftrightarrow & \color{red}{-6}x & = &4\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{4}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{-11}& = &3 \\\Leftrightarrow & 8x \color{red}{-11}\color{blue}{+11} & = &3\color{blue}{+11} \\\Leftrightarrow &8x & = &14\\\Leftrightarrow & \color{red}{8}x & = &14\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{14}{8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{4} } & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{+7}& = &9 \\\Leftrightarrow & -6x \color{red}{+7}\color{blue}{-7} & = &9\color{blue}{-7} \\\Leftrightarrow &-6x & = &2\\\Leftrightarrow & \color{red}{-6}x & = &2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{+4}& = &4 \\\Leftrightarrow & 7x \color{red}{+4}\color{blue}{-4} & = &4\color{blue}{-4} \\\Leftrightarrow &7x & = &0\\\Leftrightarrow & \color{red}{7}x & = &0\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{0}{7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{-12}& = &-7 \\\Leftrightarrow & 6x \color{red}{-12}\color{blue}{+12} & = &-7\color{blue}{+12} \\\Leftrightarrow &6x & = &5\\\Leftrightarrow & \color{red}{6}x & = &5\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{5}{6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)