Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 7x \color{red}{+11}& = &11 \\\Leftrightarrow & 7x \color{red}{+11}\color{blue}{-11} & = &11\color{blue}{-11} \\\Leftrightarrow &7x & = &0\\\Leftrightarrow & \color{red}{7}x & = &0\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{0}{7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{+11}& = &8 \\\Leftrightarrow & -10x \color{red}{+11}\color{blue}{-11} & = &8\color{blue}{-11} \\\Leftrightarrow &-10x & = &-3\\\Leftrightarrow & \color{red}{-10}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-3}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{10} } & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{-10}& = &-10 \\\Leftrightarrow & 11x \color{red}{-10}\color{blue}{+10} & = &-10\color{blue}{+10} \\\Leftrightarrow &11x & = &0\\\Leftrightarrow & \color{red}{11}x & = &0\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{0}{11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{+11}& = &-8 \\\Leftrightarrow & -4x \color{red}{+11}\color{blue}{-11} & = &-8\color{blue}{-11} \\\Leftrightarrow &-4x & = &-19\\\Leftrightarrow & \color{red}{-4}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-19}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{19}{4} } & & \\ & V = \left\{ \frac{19}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{-12}& = &5 \\\Leftrightarrow & -3x \color{red}{-12}\color{blue}{+12} & = &5\color{blue}{+12} \\\Leftrightarrow &-3x & = &17\\\Leftrightarrow & \color{red}{-3}x & = &17\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{17}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{3} } & & \\ & V = \left\{ \frac{-17}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{+7}& = &-13 \\\Leftrightarrow & 3x \color{red}{+7}\color{blue}{-7} & = &-13\color{blue}{-7} \\\Leftrightarrow &3x & = &-20\\\Leftrightarrow & \color{red}{3}x & = &-20\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-20}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{3} } & & \\ & V = \left\{ \frac{-20}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{-1}& = &-2 \\\Leftrightarrow & -11x \color{red}{-1}\color{blue}{+1} & = &-2\color{blue}{+1} \\\Leftrightarrow &-11x & = &-1\\\Leftrightarrow & \color{red}{-11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{+2}& = &9 \\\Leftrightarrow & -8x \color{red}{+2}\color{blue}{-2} & = &9\color{blue}{-2} \\\Leftrightarrow &-8x & = &7\\\Leftrightarrow & \color{red}{-8}x & = &7\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{7}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{8} } & & \\ & V = \left\{ \frac{-7}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{-2}& = &-10 \\\Leftrightarrow & -14x \color{red}{-2}\color{blue}{+2} & = &-10\color{blue}{+2} \\\Leftrightarrow &-14x & = &-8\\\Leftrightarrow & \color{red}{-14}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-8}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{-4}& = &6 \\\Leftrightarrow & -7x \color{red}{-4}\color{blue}{+4} & = &6\color{blue}{+4} \\\Leftrightarrow &-7x & = &10\\\Leftrightarrow & \color{red}{-7}x & = &10\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{10}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{7} } & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{-15}& = &12 \\\Leftrightarrow & 4x \color{red}{-15}\color{blue}{+15} & = &12\color{blue}{+15} \\\Leftrightarrow &4x & = &27\\\Leftrightarrow & \color{red}{4}x & = &27\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{27}{4} \\\Leftrightarrow & \color{green}{ x = \frac{27}{4} } & & \\ & V = \left\{ \frac{27}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{-12}& = &11 \\\Leftrightarrow & 11x \color{red}{-12}\color{blue}{+12} & = &11\color{blue}{+12} \\\Leftrightarrow &11x & = &23\\\Leftrightarrow & \color{red}{11}x & = &23\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{23}{11} \\\Leftrightarrow & \color{green}{ x = \frac{23}{11} } & & \\ & V = \left\{ \frac{23}{11} \right\} & \\\end{align}\)