Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{+4}& = &-8 \\\Leftrightarrow & 4x \color{red}{+4}\color{blue}{-4} & = &-8\color{blue}{-4} \\\Leftrightarrow &4x & = &-12\\\Leftrightarrow & \color{red}{4}x & = &-12\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-12}{4} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{-3}& = &8 \\\Leftrightarrow & -6x \color{red}{-3}\color{blue}{+3} & = &8\color{blue}{+3} \\\Leftrightarrow &-6x & = &11\\\Leftrightarrow & \color{red}{-6}x & = &11\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{11}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{6} } & & \\ & V = \left\{ \frac{-11}{6} \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{-5}& = &-12 \\\Leftrightarrow & -8x \color{red}{-5}\color{blue}{+5} & = &-12\color{blue}{+5} \\\Leftrightarrow &-8x & = &-7\\\Leftrightarrow & \color{red}{-8}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-7}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{-5}& = &9 \\\Leftrightarrow & -10x \color{red}{-5}\color{blue}{+5} & = &9\color{blue}{+5} \\\Leftrightarrow &-10x & = &14\\\Leftrightarrow & \color{red}{-10}x & = &14\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{14}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -10x \color{red}{-7}& = &6 \\\Leftrightarrow & -10x \color{red}{-7}\color{blue}{+7} & = &6\color{blue}{+7} \\\Leftrightarrow &-10x & = &13\\\Leftrightarrow & \color{red}{-10}x & = &13\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{13}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{10} } & & \\ & V = \left\{ \frac{-13}{10} \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{+10}& = &-9 \\\Leftrightarrow & -x \color{red}{+10}\color{blue}{-10} & = &-9\color{blue}{-10} \\\Leftrightarrow &-x & = &-19\\\Leftrightarrow & \color{red}{-}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-19}{-1} \\\Leftrightarrow & \color{green}{ x = 19 } & & \\ & V = \left\{ 19 \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{+9}& = &-3 \\\Leftrightarrow & 15x \color{red}{+9}\color{blue}{-9} & = &-3\color{blue}{-9} \\\Leftrightarrow &15x & = &-12\\\Leftrightarrow & \color{red}{15}x & = &-12\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-12}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{+15}& = &-13 \\\Leftrightarrow & 2x \color{red}{+15}\color{blue}{-15} & = &-13\color{blue}{-15} \\\Leftrightarrow &2x & = &-28\\\Leftrightarrow & \color{red}{2}x & = &-28\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-28}{2} \\\Leftrightarrow & \color{green}{ x = -14 } & & \\ & V = \left\{ -14 \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{-15}& = &8 \\\Leftrightarrow & -7x \color{red}{-15}\color{blue}{+15} & = &8\color{blue}{+15} \\\Leftrightarrow &-7x & = &23\\\Leftrightarrow & \color{red}{-7}x & = &23\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{23}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{7} } & & \\ & V = \left\{ \frac{-23}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{+12}& = &-5 \\\Leftrightarrow & 11x \color{red}{+12}\color{blue}{-12} & = &-5\color{blue}{-12} \\\Leftrightarrow &11x & = &-17\\\Leftrightarrow & \color{red}{11}x & = &-17\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-17}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{11} } & & \\ & V = \left\{ \frac{-17}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{-14}& = &-11 \\\Leftrightarrow & -x \color{red}{-14}\color{blue}{+14} & = &-11\color{blue}{+14} \\\Leftrightarrow &-x & = &3\\\Leftrightarrow & \color{red}{-}x & = &3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{3}{-1} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{+8}& = &-3 \\\Leftrightarrow & -11x \color{red}{+8}\color{blue}{-8} & = &-3\color{blue}{-8} \\\Leftrightarrow &-11x & = &-11\\\Leftrightarrow & \color{red}{-11}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-11}{-11} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)