Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{-13}& = & 5 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{-13}\color{blue}{+13-11x } & = & 5 \color{red}{ +11x }\color{blue}{+13-11x } \\\Leftrightarrow & 8x \color{blue}{-11x } & = & 5 \color{blue}{+13} \\\Leftrightarrow &-3x & = &18\\\Leftrightarrow & \color{red}{-3}x & = &18\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{18}{-3} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{-15}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-15}\color{blue}{+15-x } & = & 14 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 14 \color{blue}{+15} \\\Leftrightarrow &-10x & = &29\\\Leftrightarrow & \color{red}{-10}x & = &29\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{29}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{10} } & & \\ & V = \left\{ \frac{-29}{10} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{+10}& = & 1 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+10}\color{blue}{-10-7x } & = & 1 \color{red}{ +7x }\color{blue}{-10-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 1 \color{blue}{-10} \\\Leftrightarrow &-20x & = &-9\\\Leftrightarrow & \color{red}{-20}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-9}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{9}{20} } & & \\ & V = \left\{ \frac{9}{20} \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{-1}& = & 15 \color{red}{ +5x } \\\Leftrightarrow & 7x \color{red}{-1}\color{blue}{+1-5x } & = & 15 \color{red}{ +5x }\color{blue}{+1-5x } \\\Leftrightarrow & 7x \color{blue}{-5x } & = & 15 \color{blue}{+1} \\\Leftrightarrow &2x & = &16\\\Leftrightarrow & \color{red}{2}x & = &16\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{16}{2} \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{+6}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+6}\color{blue}{-6-x } & = & -14 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -14 \color{blue}{-6} \\\Leftrightarrow &-5x & = &-20\\\Leftrightarrow & \color{red}{-5}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-20}{-5} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{+2}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+2}\color{blue}{-2-x } & = & -10 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -10 \color{blue}{-2} \\\Leftrightarrow &-4x & = &-12\\\Leftrightarrow & \color{red}{-4}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-12}{-4} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{+8}& = & -10 \color{red}{ +9x } \\\Leftrightarrow & 13x \color{red}{+8}\color{blue}{-8-9x } & = & -10 \color{red}{ +9x }\color{blue}{-8-9x } \\\Leftrightarrow & 13x \color{blue}{-9x } & = & -10 \color{blue}{-8} \\\Leftrightarrow &4x & = &-18\\\Leftrightarrow & \color{red}{4}x & = &-18\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-18}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{2} } & & \\ & V = \left\{ \frac{-9}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{-1}& = & -9 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{-1}\color{blue}{+1+5x } & = & -9 \color{red}{ -5x }\color{blue}{+1+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & -9 \color{blue}{+1} \\\Leftrightarrow &8x & = &-8\\\Leftrightarrow & \color{red}{8}x & = &-8\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-8}{8} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{+1}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+1}\color{blue}{-1-x } & = & -13 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -13 \color{blue}{-1} \\\Leftrightarrow &-4x & = &-14\\\Leftrightarrow & \color{red}{-4}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-14}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{+5}& = & 8 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{+5}\color{blue}{-5-12x } & = & 8 \color{red}{ +12x }\color{blue}{-5-12x } \\\Leftrightarrow & -11x \color{blue}{-12x } & = & 8 \color{blue}{-5} \\\Leftrightarrow &-23x & = &3\\\Leftrightarrow & \color{red}{-23}x & = &3\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{3}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{23} } & & \\ & V = \left\{ \frac{-3}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{+13}& = & 5 \color{red}{ -5x } \\\Leftrightarrow & 8x \color{red}{+13}\color{blue}{-13+5x } & = & 5 \color{red}{ -5x }\color{blue}{-13+5x } \\\Leftrightarrow & 8x \color{blue}{+5x } & = & 5 \color{blue}{-13} \\\Leftrightarrow &13x & = &-8\\\Leftrightarrow & \color{red}{13}x & = &-8\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-8}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{13} } & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{-5}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-5}\color{blue}{+5-x } & = & 10 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 10 \color{blue}{+5} \\\Leftrightarrow &-15x & = &15\\\Leftrightarrow & \color{red}{-15}x & = &15\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{15}{-15} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)