Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{-1}& = &-9 \\\Leftrightarrow & -6x \color{red}{-1}\color{blue}{+1} & = &-9\color{blue}{+1} \\\Leftrightarrow &-6x & = &-8\\\Leftrightarrow & \color{red}{-6}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-8}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{-12}& = &-14 \\\Leftrightarrow & 7x \color{red}{-12}\color{blue}{+12} & = &-14\color{blue}{+12} \\\Leftrightarrow &7x & = &-2\\\Leftrightarrow & \color{red}{7}x & = &-2\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-2}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{+8}& = &-12 \\\Leftrightarrow & -12x \color{red}{+8}\color{blue}{-8} & = &-12\color{blue}{-8} \\\Leftrightarrow &-12x & = &-20\\\Leftrightarrow & \color{red}{-12}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-20}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-2}& = &-12 \\\Leftrightarrow & -15x \color{red}{-2}\color{blue}{+2} & = &-12\color{blue}{+2} \\\Leftrightarrow &-15x & = &-10\\\Leftrightarrow & \color{red}{-15}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-10}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{-13}& = &-15 \\\Leftrightarrow & 2x \color{red}{-13}\color{blue}{+13} & = &-15\color{blue}{+13} \\\Leftrightarrow &2x & = &-2\\\Leftrightarrow & \color{red}{2}x & = &-2\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-2}{2} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{-14}& = &3 \\\Leftrightarrow & -11x \color{red}{-14}\color{blue}{+14} & = &3\color{blue}{+14} \\\Leftrightarrow &-11x & = &17\\\Leftrightarrow & \color{red}{-11}x & = &17\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{17}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{11} } & & \\ & V = \left\{ \frac{-17}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{-11}& = &-3 \\\Leftrightarrow & 2x \color{red}{-11}\color{blue}{+11} & = &-3\color{blue}{+11} \\\Leftrightarrow &2x & = &8\\\Leftrightarrow & \color{red}{2}x & = &8\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{8}{2} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{+8}& = &-13 \\\Leftrightarrow & 2x \color{red}{+8}\color{blue}{-8} & = &-13\color{blue}{-8} \\\Leftrightarrow &2x & = &-21\\\Leftrightarrow & \color{red}{2}x & = &-21\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-21}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{2} } & & \\ & V = \left\{ \frac{-21}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{+15}& = &2 \\\Leftrightarrow & 2x \color{red}{+15}\color{blue}{-15} & = &2\color{blue}{-15} \\\Leftrightarrow &2x & = &-13\\\Leftrightarrow & \color{red}{2}x & = &-13\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-13}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{2} } & & \\ & V = \left\{ \frac{-13}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{-4}& = &14 \\\Leftrightarrow & -3x \color{red}{-4}\color{blue}{+4} & = &14\color{blue}{+4} \\\Leftrightarrow &-3x & = &18\\\Leftrightarrow & \color{red}{-3}x & = &18\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{18}{-3} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{+2}& = &11 \\\Leftrightarrow & 11x \color{red}{+2}\color{blue}{-2} & = &11\color{blue}{-2} \\\Leftrightarrow &11x & = &9\\\Leftrightarrow & \color{red}{11}x & = &9\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{9}{11} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{+7}& = &11 \\\Leftrightarrow & 9x \color{red}{+7}\color{blue}{-7} & = &11\color{blue}{-7} \\\Leftrightarrow &9x & = &4\\\Leftrightarrow & \color{red}{9}x & = &4\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{4}{9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{9} } & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)