Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{+11}& = &14 \\\Leftrightarrow & 5x \color{red}{+11}\color{blue}{-11} & = &14\color{blue}{-11} \\\Leftrightarrow &5x & = &3\\\Leftrightarrow & \color{red}{5}x & = &3\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{3}{5} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{+3}& = &8 \\\Leftrightarrow & 11x \color{red}{+3}\color{blue}{-3} & = &8\color{blue}{-3} \\\Leftrightarrow &11x & = &5\\\Leftrightarrow & \color{red}{11}x & = &5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{+11}& = &13 \\\Leftrightarrow & 2x \color{red}{+11}\color{blue}{-11} & = &13\color{blue}{-11} \\\Leftrightarrow &2x & = &2\\\Leftrightarrow & \color{red}{2}x & = &2\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{2}{2} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{-12}& = &11 \\\Leftrightarrow & 9x \color{red}{-12}\color{blue}{+12} & = &11\color{blue}{+12} \\\Leftrightarrow &9x & = &23\\\Leftrightarrow & \color{red}{9}x & = &23\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{23}{9} \\\Leftrightarrow & \color{green}{ x = \frac{23}{9} } & & \\ & V = \left\{ \frac{23}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{-7}& = &-9 \\\Leftrightarrow & 10x \color{red}{-7}\color{blue}{+7} & = &-9\color{blue}{+7} \\\Leftrightarrow &10x & = &-2\\\Leftrightarrow & \color{red}{10}x & = &-2\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-2}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{+4}& = &4 \\\Leftrightarrow & -4x \color{red}{+4}\color{blue}{-4} & = &4\color{blue}{-4} \\\Leftrightarrow &-4x & = &0\\\Leftrightarrow & \color{red}{-4}x & = &0\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{0}{-4} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{-3}& = &14 \\\Leftrightarrow & 2x \color{red}{-3}\color{blue}{+3} & = &14\color{blue}{+3} \\\Leftrightarrow &2x & = &17\\\Leftrightarrow & \color{red}{2}x & = &17\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{17}{2} \\\Leftrightarrow & \color{green}{ x = \frac{17}{2} } & & \\ & V = \left\{ \frac{17}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{-11}& = &15 \\\Leftrightarrow & 6x \color{red}{-11}\color{blue}{+11} & = &15\color{blue}{+11} \\\Leftrightarrow &6x & = &26\\\Leftrightarrow & \color{red}{6}x & = &26\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{26}{6} \\\Leftrightarrow & \color{green}{ x = \frac{13}{3} } & & \\ & V = \left\{ \frac{13}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{+14}& = &-4 \\\Leftrightarrow & -14x \color{red}{+14}\color{blue}{-14} & = &-4\color{blue}{-14} \\\Leftrightarrow &-14x & = &-18\\\Leftrightarrow & \color{red}{-14}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-18}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{9}{7} } & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{+11}& = &11 \\\Leftrightarrow & -10x \color{red}{+11}\color{blue}{-11} & = &11\color{blue}{-11} \\\Leftrightarrow &-10x & = &0\\\Leftrightarrow & \color{red}{-10}x & = &0\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{0}{-10} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{+12}& = &3 \\\Leftrightarrow & -11x \color{red}{+12}\color{blue}{-12} & = &3\color{blue}{-12} \\\Leftrightarrow &-11x & = &-9\\\Leftrightarrow & \color{red}{-11}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-9}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{+1}& = &-14 \\\Leftrightarrow & -14x \color{red}{+1}\color{blue}{-1} & = &-14\color{blue}{-1} \\\Leftrightarrow &-14x & = &-15\\\Leftrightarrow & \color{red}{-14}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-15}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{15}{14} } & & \\ & V = \left\{ \frac{15}{14} \right\} & \\\end{align}\)