Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{-9}& = &-11 \\\Leftrightarrow & 9x \color{red}{-9}\color{blue}{+9} & = &-11\color{blue}{+9} \\\Leftrightarrow &9x & = &-2\\\Leftrightarrow & \color{red}{9}x & = &-2\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-2}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{-7}& = &5 \\\Leftrightarrow & 12x \color{red}{-7}\color{blue}{+7} & = &5\color{blue}{+7} \\\Leftrightarrow &12x & = &12\\\Leftrightarrow & \color{red}{12}x & = &12\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{12}{12} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{+14}& = &-2 \\\Leftrightarrow & -8x \color{red}{+14}\color{blue}{-14} & = &-2\color{blue}{-14} \\\Leftrightarrow &-8x & = &-16\\\Leftrightarrow & \color{red}{-8}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-16}{-8} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{-5}& = &13 \\\Leftrightarrow & -x \color{red}{-5}\color{blue}{+5} & = &13\color{blue}{+5} \\\Leftrightarrow &-x & = &18\\\Leftrightarrow & \color{red}{-}x & = &18\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{18}{-1} \\\Leftrightarrow & \color{green}{ x = -18 } & & \\ & V = \left\{ -18 \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{-8}& = &-12 \\\Leftrightarrow & 4x \color{red}{-8}\color{blue}{+8} & = &-12\color{blue}{+8} \\\Leftrightarrow &4x & = &-4\\\Leftrightarrow & \color{red}{4}x & = &-4\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-4}{4} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{+9}& = &3 \\\Leftrightarrow & 15x \color{red}{+9}\color{blue}{-9} & = &3\color{blue}{-9} \\\Leftrightarrow &15x & = &-6\\\Leftrightarrow & \color{red}{15}x & = &-6\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-6}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{+2}& = &-2 \\\Leftrightarrow & -3x \color{red}{+2}\color{blue}{-2} & = &-2\color{blue}{-2} \\\Leftrightarrow &-3x & = &-4\\\Leftrightarrow & \color{red}{-3}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-4}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{+7}& = &-9 \\\Leftrightarrow & 9x \color{red}{+7}\color{blue}{-7} & = &-9\color{blue}{-7} \\\Leftrightarrow &9x & = &-16\\\Leftrightarrow & \color{red}{9}x & = &-16\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-16}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{9} } & & \\ & V = \left\{ \frac{-16}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{+15}& = &8 \\\Leftrightarrow & 9x \color{red}{+15}\color{blue}{-15} & = &8\color{blue}{-15} \\\Leftrightarrow &9x & = &-7\\\Leftrightarrow & \color{red}{9}x & = &-7\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-7}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{9} } & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{-4}& = &-7 \\\Leftrightarrow & 12x \color{red}{-4}\color{blue}{+4} & = &-7\color{blue}{+4} \\\Leftrightarrow &12x & = &-3\\\Leftrightarrow & \color{red}{12}x & = &-3\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-3}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{-2}& = &-13 \\\Leftrightarrow & 10x \color{red}{-2}\color{blue}{+2} & = &-13\color{blue}{+2} \\\Leftrightarrow &10x & = &-11\\\Leftrightarrow & \color{red}{10}x & = &-11\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-11}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{10} } & & \\ & V = \left\{ \frac{-11}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{-1}& = &-5 \\\Leftrightarrow & 2x \color{red}{-1}\color{blue}{+1} & = &-5\color{blue}{+1} \\\Leftrightarrow &2x & = &-4\\\Leftrightarrow & \color{red}{2}x & = &-4\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-4}{2} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)