Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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