Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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