Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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