Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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