Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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