Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{-2}& = & 8 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{-2}\color{blue}{+2-7x } & = & 8 \color{red}{ +7x }\color{blue}{+2-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & 8 \color{blue}{+2} \\\Leftrightarrow &-5x & = &10\\\Leftrightarrow & \color{red}{-5}x & = &10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{10}{-5} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{-11}& = & -6 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{-11}\color{blue}{+11-11x } & = & -6 \color{red}{ +11x }\color{blue}{+11-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & -6 \color{blue}{+11} \\\Leftrightarrow &-21x & = &5\\\Leftrightarrow & \color{red}{-21}x & = &5\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{5}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{21} } & & \\ & V = \left\{ \frac{-5}{21} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{+1}& = & 13 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{+1}\color{blue}{-1-14x } & = & 13 \color{red}{ +14x }\color{blue}{-1-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & 13 \color{blue}{-1} \\\Leftrightarrow &-27x & = &12\\\Leftrightarrow & \color{red}{-27}x & = &12\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{12}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{9} } & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{+7}& = & 9 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+7}\color{blue}{-7+2x } & = & 9 \color{red}{ -2x }\color{blue}{-7+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & 9 \color{blue}{-7} \\\Leftrightarrow &17x & = &2\\\Leftrightarrow & \color{red}{17}x & = &2\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{2}{17} \\\Leftrightarrow & \color{green}{ x = \frac{2}{17} } & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{-9}& = & 9 \color{red}{ +10x } \\\Leftrightarrow & -13x \color{red}{-9}\color{blue}{+9-10x } & = & 9 \color{red}{ +10x }\color{blue}{+9-10x } \\\Leftrightarrow & -13x \color{blue}{-10x } & = & 9 \color{blue}{+9} \\\Leftrightarrow &-23x & = &18\\\Leftrightarrow & \color{red}{-23}x & = &18\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{18}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{23} } & & \\ & V = \left\{ \frac{-18}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{-12}& = & -2 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-12}\color{blue}{+12+8x } & = & -2 \color{red}{ -8x }\color{blue}{+12+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & -2 \color{blue}{+12} \\\Leftrightarrow &11x & = &10\\\Leftrightarrow & \color{red}{11}x & = &10\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{10}{11} \\\Leftrightarrow & \color{green}{ x = \frac{10}{11} } & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{+8}& = & 5 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{+8}\color{blue}{-8+14x } & = & 5 \color{red}{ -14x }\color{blue}{-8+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & 5 \color{blue}{-8} \\\Leftrightarrow &29x & = &-3\\\Leftrightarrow & \color{red}{29}x & = &-3\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{-3}{29} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{29} } & & \\ & V = \left\{ \frac{-3}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & -3x \color{red}{-11}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-11}\color{blue}{+11-x } & = & 15 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 15 \color{blue}{+11} \\\Leftrightarrow &-4x & = &26\\\Leftrightarrow & \color{red}{-4}x & = &26\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{26}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{2} } & & \\ & V = \left\{ \frac{-13}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{+2}& = & 3 \color{red}{ -10x } \\\Leftrightarrow & x \color{red}{+2}\color{blue}{-2+10x } & = & 3 \color{red}{ -10x }\color{blue}{-2+10x } \\\Leftrightarrow & x \color{blue}{+10x } & = & 3 \color{blue}{-2} \\\Leftrightarrow &11x & = &1\\\Leftrightarrow & \color{red}{11}x & = &1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{-2}& = & -13 \color{red}{ -2x } \\\Leftrightarrow & 9x \color{red}{-2}\color{blue}{+2+2x } & = & -13 \color{red}{ -2x }\color{blue}{+2+2x } \\\Leftrightarrow & 9x \color{blue}{+2x } & = & -13 \color{blue}{+2} \\\Leftrightarrow &11x & = &-11\\\Leftrightarrow & \color{red}{11}x & = &-11\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-11}{11} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{+11}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+11}\color{blue}{-11-x } & = & -10 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -10 \color{blue}{-11} \\\Leftrightarrow &-11x & = &-21\\\Leftrightarrow & \color{red}{-11}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-21}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{21}{11} } & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{+9}& = & 11 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{+9}\color{blue}{-9-11x } & = & 11 \color{red}{ +11x }\color{blue}{-9-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & 11 \color{blue}{-9} \\\Leftrightarrow &-5x & = &2\\\Leftrightarrow & \color{red}{-5}x & = &2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)