Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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