Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{-15}& = &9 \\\Leftrightarrow & 9x \color{red}{-15}\color{blue}{+15} & = &9\color{blue}{+15} \\\Leftrightarrow &9x & = &24\\\Leftrightarrow & \color{red}{9}x & = &24\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{24}{9} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{+5}& = &4 \\\Leftrightarrow & -x \color{red}{+5}\color{blue}{-5} & = &4\color{blue}{-5} \\\Leftrightarrow &-x & = &-1\\\Leftrightarrow & \color{red}{-}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-1}{-1} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{-2}& = &5 \\\Leftrightarrow & 13x \color{red}{-2}\color{blue}{+2} & = &5\color{blue}{+2} \\\Leftrightarrow &13x & = &7\\\Leftrightarrow & \color{red}{13}x & = &7\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{7}{13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{+11}& = &5 \\\Leftrightarrow & -8x \color{red}{+11}\color{blue}{-11} & = &5\color{blue}{-11} \\\Leftrightarrow &-8x & = &-6\\\Leftrightarrow & \color{red}{-8}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-6}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{+4}& = &-13 \\\Leftrightarrow & -6x \color{red}{+4}\color{blue}{-4} & = &-13\color{blue}{-4} \\\Leftrightarrow &-6x & = &-17\\\Leftrightarrow & \color{red}{-6}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-17}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{17}{6} } & & \\ & V = \left\{ \frac{17}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{+4}& = &-9 \\\Leftrightarrow & 11x \color{red}{+4}\color{blue}{-4} & = &-9\color{blue}{-4} \\\Leftrightarrow &11x & = &-13\\\Leftrightarrow & \color{red}{11}x & = &-13\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-13}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{11} } & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{+1}& = &-15 \\\Leftrightarrow & -15x \color{red}{+1}\color{blue}{-1} & = &-15\color{blue}{-1} \\\Leftrightarrow &-15x & = &-16\\\Leftrightarrow & \color{red}{-15}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-16}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{16}{15} } & & \\ & V = \left\{ \frac{16}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{-4}& = &-12 \\\Leftrightarrow & 8x \color{red}{-4}\color{blue}{+4} & = &-12\color{blue}{+4} \\\Leftrightarrow &8x & = &-8\\\Leftrightarrow & \color{red}{8}x & = &-8\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-8}{8} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{+9}& = &-8 \\\Leftrightarrow & -12x \color{red}{+9}\color{blue}{-9} & = &-8\color{blue}{-9} \\\Leftrightarrow &-12x & = &-17\\\Leftrightarrow & \color{red}{-12}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-17}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{17}{12} } & & \\ & V = \left\{ \frac{17}{12} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{-11}& = &-1 \\\Leftrightarrow & -6x \color{red}{-11}\color{blue}{+11} & = &-1\color{blue}{+11} \\\Leftrightarrow &-6x & = &10\\\Leftrightarrow & \color{red}{-6}x & = &10\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{10}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{-14}& = &3 \\\Leftrightarrow & -10x \color{red}{-14}\color{blue}{+14} & = &3\color{blue}{+14} \\\Leftrightarrow &-10x & = &17\\\Leftrightarrow & \color{red}{-10}x & = &17\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{17}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{10} } & & \\ & V = \left\{ \frac{-17}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{+12}& = &5 \\\Leftrightarrow & -3x \color{red}{+12}\color{blue}{-12} & = &5\color{blue}{-12} \\\Leftrightarrow &-3x & = &-7\\\Leftrightarrow & \color{red}{-3}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-7}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)