Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{-2}& = &13 \\\Leftrightarrow & 6x \color{red}{-2}\color{blue}{+2} & = &13\color{blue}{+2} \\\Leftrightarrow &6x & = &15\\\Leftrightarrow & \color{red}{6}x & = &15\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{15}{6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{-5}& = &10 \\\Leftrightarrow & 10x \color{red}{-5}\color{blue}{+5} & = &10\color{blue}{+5} \\\Leftrightarrow &10x & = &15\\\Leftrightarrow & \color{red}{10}x & = &15\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{15}{10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{-7}& = &3 \\\Leftrightarrow & -4x \color{red}{-7}\color{blue}{+7} & = &3\color{blue}{+7} \\\Leftrightarrow &-4x & = &10\\\Leftrightarrow & \color{red}{-4}x & = &10\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{10}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{-10}& = &12 \\\Leftrightarrow & 10x \color{red}{-10}\color{blue}{+10} & = &12\color{blue}{+10} \\\Leftrightarrow &10x & = &22\\\Leftrightarrow & \color{red}{10}x & = &22\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{22}{10} \\\Leftrightarrow & \color{green}{ x = \frac{11}{5} } & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{-7}& = &-10 \\\Leftrightarrow & 11x \color{red}{-7}\color{blue}{+7} & = &-10\color{blue}{+7} \\\Leftrightarrow &11x & = &-3\\\Leftrightarrow & \color{red}{11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-3}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{-4}& = &-1 \\\Leftrightarrow & -2x \color{red}{-4}\color{blue}{+4} & = &-1\color{blue}{+4} \\\Leftrightarrow &-2x & = &3\\\Leftrightarrow & \color{red}{-2}x & = &3\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{3}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{+2}& = &11 \\\Leftrightarrow & -11x \color{red}{+2}\color{blue}{-2} & = &11\color{blue}{-2} \\\Leftrightarrow &-11x & = &9\\\Leftrightarrow & \color{red}{-11}x & = &9\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{9}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{11} } & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{-9}& = &-3 \\\Leftrightarrow & 2x \color{red}{-9}\color{blue}{+9} & = &-3\color{blue}{+9} \\\Leftrightarrow &2x & = &6\\\Leftrightarrow & \color{red}{2}x & = &6\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{6}{2} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{-5}& = &-15 \\\Leftrightarrow & -8x \color{red}{-5}\color{blue}{+5} & = &-15\color{blue}{+5} \\\Leftrightarrow &-8x & = &-10\\\Leftrightarrow & \color{red}{-8}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-10}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{+11}& = &3 \\\Leftrightarrow & -x \color{red}{+11}\color{blue}{-11} & = &3\color{blue}{-11} \\\Leftrightarrow &-x & = &-8\\\Leftrightarrow & \color{red}{-}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-8}{-1} \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{-2}& = &9 \\\Leftrightarrow & 4x \color{red}{-2}\color{blue}{+2} & = &9\color{blue}{+2} \\\Leftrightarrow &4x & = &11\\\Leftrightarrow & \color{red}{4}x & = &11\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{11}{4} \\\Leftrightarrow & \color{green}{ x = \frac{11}{4} } & & \\ & V = \left\{ \frac{11}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{-14}& = &-12 \\\Leftrightarrow & -9x \color{red}{-14}\color{blue}{+14} & = &-12\color{blue}{+14} \\\Leftrightarrow &-9x & = &2\\\Leftrightarrow & \color{red}{-9}x & = &2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)