Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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