Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{-10}& = &12 \\\Leftrightarrow & 8x \color{red}{-10}\color{blue}{+10} & = &12\color{blue}{+10} \\\Leftrightarrow &8x & = &22\\\Leftrightarrow & \color{red}{8}x & = &22\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{22}{8} \\\Leftrightarrow & \color{green}{ x = \frac{11}{4} } & & \\ & V = \left\{ \frac{11}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{+9}& = &1 \\\Leftrightarrow & 14x \color{red}{+9}\color{blue}{-9} & = &1\color{blue}{-9} \\\Leftrightarrow &14x & = &-8\\\Leftrightarrow & \color{red}{14}x & = &-8\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-8}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{+5}& = &-2 \\\Leftrightarrow & -5x \color{red}{+5}\color{blue}{-5} & = &-2\color{blue}{-5} \\\Leftrightarrow &-5x & = &-7\\\Leftrightarrow & \color{red}{-5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & x \color{red}{-12}& = &-13 \\\Leftrightarrow & x \color{red}{-12}\color{blue}{+12} & = &-13\color{blue}{+12} \\\Leftrightarrow &x & = &-1\\\Leftrightarrow & \color{red}{}x & = &-1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -1 \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{+14}& = &11 \\\Leftrightarrow & 9x \color{red}{+14}\color{blue}{-14} & = &11\color{blue}{-14} \\\Leftrightarrow &9x & = &-3\\\Leftrightarrow & \color{red}{9}x & = &-3\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-3}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{+11}& = &5 \\\Leftrightarrow & -5x \color{red}{+11}\color{blue}{-11} & = &5\color{blue}{-11} \\\Leftrightarrow &-5x & = &-6\\\Leftrightarrow & \color{red}{-5}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-6}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{+9}& = &13 \\\Leftrightarrow & -10x \color{red}{+9}\color{blue}{-9} & = &13\color{blue}{-9} \\\Leftrightarrow &-10x & = &4\\\Leftrightarrow & \color{red}{-10}x & = &4\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{4}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{-7}& = &-5 \\\Leftrightarrow & -14x \color{red}{-7}\color{blue}{+7} & = &-5\color{blue}{+7} \\\Leftrightarrow &-14x & = &2\\\Leftrightarrow & \color{red}{-14}x & = &2\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{2}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{+11}& = &-7 \\\Leftrightarrow & -11x \color{red}{+11}\color{blue}{-11} & = &-7\color{blue}{-11} \\\Leftrightarrow &-11x & = &-18\\\Leftrightarrow & \color{red}{-11}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-18}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{18}{11} } & & \\ & V = \left\{ \frac{18}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{+1}& = &1 \\\Leftrightarrow & 9x \color{red}{+1}\color{blue}{-1} & = &1\color{blue}{-1} \\\Leftrightarrow &9x & = &0\\\Leftrightarrow & \color{red}{9}x & = &0\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{0}{9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{-9}& = &-4 \\\Leftrightarrow & 7x \color{red}{-9}\color{blue}{+9} & = &-4\color{blue}{+9} \\\Leftrightarrow &7x & = &5\\\Leftrightarrow & \color{red}{7}x & = &5\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{5}{7} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{-12}& = &5 \\\Leftrightarrow & 11x \color{red}{-12}\color{blue}{+12} & = &5\color{blue}{+12} \\\Leftrightarrow &11x & = &17\\\Leftrightarrow & \color{red}{11}x & = &17\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{17}{11} \\\Leftrightarrow & \color{green}{ x = \frac{17}{11} } & & \\ & V = \left\{ \frac{17}{11} \right\} & \\\end{align}\)