Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{+1}& = & -11 \color{red}{ +4x } \\\Leftrightarrow & 15x \color{red}{+1}\color{blue}{-1-4x } & = & -11 \color{red}{ +4x }\color{blue}{-1-4x } \\\Leftrightarrow & 15x \color{blue}{-4x } & = & -11 \color{blue}{-1} \\\Leftrightarrow &11x & = &-12\\\Leftrightarrow & \color{red}{11}x & = &-12\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-12}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{11} } & & \\ & V = \left\{ \frac{-12}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{-3}& = & -10 \color{red}{ -7x } \\\Leftrightarrow & 11x \color{red}{-3}\color{blue}{+3+7x } & = & -10 \color{red}{ -7x }\color{blue}{+3+7x } \\\Leftrightarrow & 11x \color{blue}{+7x } & = & -10 \color{blue}{+3} \\\Leftrightarrow &18x & = &-7\\\Leftrightarrow & \color{red}{18}x & = &-7\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}} & = & \frac{-7}{18} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{18} } & & \\ & V = \left\{ \frac{-7}{18} \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{-14}& = & -2 \color{red}{ +4x } \\\Leftrightarrow & 3x \color{red}{-14}\color{blue}{+14-4x } & = & -2 \color{red}{ +4x }\color{blue}{+14-4x } \\\Leftrightarrow & 3x \color{blue}{-4x } & = & -2 \color{blue}{+14} \\\Leftrightarrow &-x & = &12\\\Leftrightarrow & \color{red}{-}x & = &12\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{12}{-1} \\\Leftrightarrow & \color{green}{ x = -12 } & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{-4}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-4}\color{blue}{+4-x } & = & 5 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 5 \color{blue}{+4} \\\Leftrightarrow &-6x & = &9\\\Leftrightarrow & \color{red}{-6}x & = &9\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{9}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{+10}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+10}\color{blue}{-10-x } & = & -15 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -15 \color{blue}{-10} \\\Leftrightarrow &-8x & = &-25\\\Leftrightarrow & \color{red}{-8}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-25}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{25}{8} } & & \\ & V = \left\{ \frac{25}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{-5}& = & 7 \color{red}{ +12x } \\\Leftrightarrow & 7x \color{red}{-5}\color{blue}{+5-12x } & = & 7 \color{red}{ +12x }\color{blue}{+5-12x } \\\Leftrightarrow & 7x \color{blue}{-12x } & = & 7 \color{blue}{+5} \\\Leftrightarrow &-5x & = &12\\\Leftrightarrow & \color{red}{-5}x & = &12\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{12}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{5} } & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{+15}& = & -3 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+15}\color{blue}{-15+13x } & = & -3 \color{red}{ -13x }\color{blue}{-15+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & -3 \color{blue}{-15} \\\Leftrightarrow &20x & = &-18\\\Leftrightarrow & \color{red}{20}x & = &-18\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-18}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{10} } & & \\ & V = \left\{ \frac{-9}{10} \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{+6}& = & 2 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{+6}\color{blue}{-6-6x } & = & 2 \color{red}{ +6x }\color{blue}{-6-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & 2 \color{blue}{-6} \\\Leftrightarrow &-11x & = &-4\\\Leftrightarrow & \color{red}{-11}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-4}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{4}{11} } & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{+1}& = & -4 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{+1}\color{blue}{-1+3x } & = & -4 \color{red}{ -3x }\color{blue}{-1+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & -4 \color{blue}{-1} \\\Leftrightarrow &7x & = &-5\\\Leftrightarrow & \color{red}{7}x & = &-5\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-5}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{+14}& = & 9 \color{red}{ -5x } \\\Leftrightarrow & 13x \color{red}{+14}\color{blue}{-14+5x } & = & 9 \color{red}{ -5x }\color{blue}{-14+5x } \\\Leftrightarrow & 13x \color{blue}{+5x } & = & 9 \color{blue}{-14} \\\Leftrightarrow &18x & = &-5\\\Leftrightarrow & \color{red}{18}x & = &-5\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}} & = & \frac{-5}{18} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{18} } & & \\ & V = \left\{ \frac{-5}{18} \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{+2}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+2}\color{blue}{-2-x } & = & -3 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -3 \color{blue}{-2} \\\Leftrightarrow &7x & = &-5\\\Leftrightarrow & \color{red}{7}x & = &-5\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-5}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{+8}& = & -5 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{+8}\color{blue}{-8-3x } & = & -5 \color{red}{ +3x }\color{blue}{-8-3x } \\\Leftrightarrow & -2x \color{blue}{-3x } & = & -5 \color{blue}{-8} \\\Leftrightarrow &-5x & = &-13\\\Leftrightarrow & \color{red}{-5}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-13}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{13}{5} } & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)