Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{-1}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & 3x \color{red}{-1}\color{blue}{+1-13x } & = & 9 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & 3x \color{blue}{-13x } & = & 9 \color{blue}{+1} \\\Leftrightarrow &-10x & = &10\\\Leftrightarrow & \color{red}{-10}x & = &10\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{10}{-10} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{-1}& = & 4 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{-1}\color{blue}{+1+13x } & = & 4 \color{red}{ -13x }\color{blue}{+1+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & 4 \color{blue}{+1} \\\Leftrightarrow &20x & = &5\\\Leftrightarrow & \color{red}{20}x & = &5\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{5}{20} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{+7}& = & 15 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{+7}\color{blue}{-7-9x } & = & 15 \color{red}{ +9x }\color{blue}{-7-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & 15 \color{blue}{-7} \\\Leftrightarrow &5x & = &8\\\Leftrightarrow & \color{red}{5}x & = &8\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{8}{5} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{-13}& = & -12 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{-13}\color{blue}{+13+7x } & = & -12 \color{red}{ -7x }\color{blue}{+13+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & -12 \color{blue}{+13} \\\Leftrightarrow &22x & = &1\\\Leftrightarrow & \color{red}{22}x & = &1\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{1}{22} \\\Leftrightarrow & \color{green}{ x = \frac{1}{22} } & & \\ & V = \left\{ \frac{1}{22} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{-6}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-6}\color{blue}{+6-x } & = & -14 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -14 \color{blue}{+6} \\\Leftrightarrow &-3x & = &-8\\\Leftrightarrow & \color{red}{-3}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{-2}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-2}\color{blue}{+2-x } & = & 8 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 8 \color{blue}{+2} \\\Leftrightarrow &-6x & = &10\\\Leftrightarrow & \color{red}{-6}x & = &10\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{10}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{-4}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-4}\color{blue}{+4-x } & = & 11 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 11 \color{blue}{+4} \\\Leftrightarrow &-7x & = &15\\\Leftrightarrow & \color{red}{-7}x & = &15\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{15}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{7} } & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{-11}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{-11}\color{blue}{+11-x } & = & -9 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & -9 \color{blue}{+11} \\\Leftrightarrow &8x & = &2\\\Leftrightarrow & \color{red}{8}x & = &2\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{2}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{+1}& = & 5 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+1}\color{blue}{-1-x } & = & 5 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 5 \color{blue}{-1} \\\Leftrightarrow &11x & = &4\\\Leftrightarrow & \color{red}{11}x & = &4\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{4}{11} \\\Leftrightarrow & \color{green}{ x = \frac{4}{11} } & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{-9}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-9}\color{blue}{+9-x } & = & -14 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -14 \color{blue}{+9} \\\Leftrightarrow &-6x & = &-5\\\Leftrightarrow & \color{red}{-6}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-5}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{+11}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+11}\color{blue}{-11-x } & = & -9 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -9 \color{blue}{-11} \\\Leftrightarrow &-15x & = &-20\\\Leftrightarrow & \color{red}{-15}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-20}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{-7}& = & -9 \color{red}{ -4x } \\\Leftrightarrow & 13x \color{red}{-7}\color{blue}{+7+4x } & = & -9 \color{red}{ -4x }\color{blue}{+7+4x } \\\Leftrightarrow & 13x \color{blue}{+4x } & = & -9 \color{blue}{+7} \\\Leftrightarrow &17x & = &-2\\\Leftrightarrow & \color{red}{17}x & = &-2\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-2}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{17} } & & \\ & V = \left\{ \frac{-2}{17} \right\} & \\\end{align}\)