Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{-13}& = & -13 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{-13}\color{blue}{+13+5x } & = & -13 \color{red}{ -5x }\color{blue}{+13+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & -13 \color{blue}{+13} \\\Leftrightarrow &8x & = &0\\\Leftrightarrow & \color{red}{8}x & = &0\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{0}{8} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{-11}& = & -13 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-11}\color{blue}{+11-13x } & = & -13 \color{red}{ +13x }\color{blue}{+11-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -13 \color{blue}{+11} \\\Leftrightarrow &-25x & = &-2\\\Leftrightarrow & \color{red}{-25}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-2}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{2}{25} } & & \\ & V = \left\{ \frac{2}{25} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{+15}& = & 10 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{+15}\color{blue}{-15+10x } & = & 10 \color{red}{ -10x }\color{blue}{-15+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & 10 \color{blue}{-15} \\\Leftrightarrow &21x & = &-5\\\Leftrightarrow & \color{red}{21}x & = &-5\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{-5}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{21} } & & \\ & V = \left\{ \frac{-5}{21} \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{-9}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-9}\color{blue}{+9-x } & = & 13 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 13 \color{blue}{+9} \\\Leftrightarrow &-9x & = &22\\\Leftrightarrow & \color{red}{-9}x & = &22\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{22}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{9} } & & \\ & V = \left\{ \frac{-22}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & -10x \color{red}{-13}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-13}\color{blue}{+13-x } & = & -7 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -7 \color{blue}{+13} \\\Leftrightarrow &-11x & = &6\\\Leftrightarrow & \color{red}{-11}x & = &6\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{6}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{-2}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-2}\color{blue}{+2-x } & = & 6 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 6 \color{blue}{+2} \\\Leftrightarrow &-14x & = &8\\\Leftrightarrow & \color{red}{-14}x & = &8\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{8}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{-8}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-8}\color{blue}{+8-x } & = & 2 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 2 \color{blue}{+8} \\\Leftrightarrow &-5x & = &10\\\Leftrightarrow & \color{red}{-5}x & = &10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{10}{-5} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{+4}& = & 8 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+4}\color{blue}{-4+11x } & = & 8 \color{red}{ -11x }\color{blue}{-4+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 8 \color{blue}{-4} \\\Leftrightarrow &23x & = &4\\\Leftrightarrow & \color{red}{23}x & = &4\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{4}{23} \\\Leftrightarrow & \color{green}{ x = \frac{4}{23} } & & \\ & V = \left\{ \frac{4}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{-13}& = & -2 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-13}\color{blue}{+13+11x } & = & -2 \color{red}{ -11x }\color{blue}{+13+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -2 \color{blue}{+13} \\\Leftrightarrow &23x & = &11\\\Leftrightarrow & \color{red}{23}x & = &11\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{11}{23} \\\Leftrightarrow & \color{green}{ x = \frac{11}{23} } & & \\ & V = \left\{ \frac{11}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{-8}& = & 1 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-8}\color{blue}{+8+13x } & = & 1 \color{red}{ -13x }\color{blue}{+8+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 1 \color{blue}{+8} \\\Leftrightarrow &27x & = &9\\\Leftrightarrow & \color{red}{27}x & = &9\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{9}{27} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{-7}& = & 12 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{-7}\color{blue}{+7-6x } & = & 12 \color{red}{ +6x }\color{blue}{+7-6x } \\\Leftrightarrow & -11x \color{blue}{-6x } & = & 12 \color{blue}{+7} \\\Leftrightarrow &-17x & = &19\\\Leftrightarrow & \color{red}{-17}x & = &19\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{19}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{17} } & & \\ & V = \left\{ \frac{-19}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{-2}& = & -14 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{-2}\color{blue}{+2-6x } & = & -14 \color{red}{ +6x }\color{blue}{+2-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & -14 \color{blue}{+2} \\\Leftrightarrow &-11x & = &-12\\\Leftrightarrow & \color{red}{-11}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-12}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{12}{11} } & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)