Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{-15}& = & 1 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{-15}\color{blue}{+15-11x } & = & 1 \color{red}{ +11x }\color{blue}{+15-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & 1 \color{blue}{+15} \\\Leftrightarrow &-21x & = &16\\\Leftrightarrow & \color{red}{-21}x & = &16\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{16}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{21} } & & \\ & V = \left\{ \frac{-16}{21} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{-7}& = & 10 \color{red}{ +11x } \\\Leftrightarrow & -2x \color{red}{-7}\color{blue}{+7-11x } & = & 10 \color{red}{ +11x }\color{blue}{+7-11x } \\\Leftrightarrow & -2x \color{blue}{-11x } & = & 10 \color{blue}{+7} \\\Leftrightarrow &-13x & = &17\\\Leftrightarrow & \color{red}{-13}x & = &17\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{17}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{13} } & & \\ & V = \left\{ \frac{-17}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{-8}& = & 6 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{-8}\color{blue}{+8-3x } & = & 6 \color{red}{ +3x }\color{blue}{+8-3x } \\\Leftrightarrow & 2x \color{blue}{-3x } & = & 6 \color{blue}{+8} \\\Leftrightarrow &-x & = &14\\\Leftrightarrow & \color{red}{-}x & = &14\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{14}{-1} \\\Leftrightarrow & \color{green}{ x = -14 } & & \\ & V = \left\{ -14 \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{-9}& = & -14 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-9}\color{blue}{+9+13x } & = & -14 \color{red}{ -13x }\color{blue}{+9+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -14 \color{blue}{+9} \\\Leftrightarrow &23x & = &-5\\\Leftrightarrow & \color{red}{23}x & = &-5\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-5}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{23} } & & \\ & V = \left\{ \frac{-5}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{+2}& = & 4 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{+2}\color{blue}{-2+13x } & = & 4 \color{red}{ -13x }\color{blue}{-2+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & 4 \color{blue}{-2} \\\Leftrightarrow &22x & = &2\\\Leftrightarrow & \color{red}{22}x & = &2\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{2}{22} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{+4}& = & 7 \color{red}{ +10x } \\\Leftrightarrow & 3x \color{red}{+4}\color{blue}{-4-10x } & = & 7 \color{red}{ +10x }\color{blue}{-4-10x } \\\Leftrightarrow & 3x \color{blue}{-10x } & = & 7 \color{blue}{-4} \\\Leftrightarrow &-7x & = &3\\\Leftrightarrow & \color{red}{-7}x & = &3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{+15}& = & -1 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{+15}\color{blue}{-15-4x } & = & -1 \color{red}{ +4x }\color{blue}{-15-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & -1 \color{blue}{-15} \\\Leftrightarrow &-7x & = &-16\\\Leftrightarrow & \color{red}{-7}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-16}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{16}{7} } & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{-5}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-5}\color{blue}{+5-x } & = & -1 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -1 \color{blue}{+5} \\\Leftrightarrow &-14x & = &4\\\Leftrightarrow & \color{red}{-14}x & = &4\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{4}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{+5}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+5}\color{blue}{-5-x } & = & 7 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 7 \color{blue}{-5} \\\Leftrightarrow &-16x & = &2\\\Leftrightarrow & \color{red}{-16}x & = &2\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{2}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{+10}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+10}\color{blue}{-10-x } & = & -9 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -9 \color{blue}{-10} \\\Leftrightarrow &-11x & = &-19\\\Leftrightarrow & \color{red}{-11}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-19}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{19}{11} } & & \\ & V = \left\{ \frac{19}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{-8}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-8}\color{blue}{+8-x } & = & 14 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 14 \color{blue}{+8} \\\Leftrightarrow &-13x & = &22\\\Leftrightarrow & \color{red}{-13}x & = &22\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{22}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{13} } & & \\ & V = \left\{ \frac{-22}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{-8}& = & 10 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{-8}\color{blue}{+8-5x } & = & 10 \color{red}{ +5x }\color{blue}{+8-5x } \\\Leftrightarrow & -2x \color{blue}{-5x } & = & 10 \color{blue}{+8} \\\Leftrightarrow &-7x & = &18\\\Leftrightarrow & \color{red}{-7}x & = &18\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{18}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{7} } & & \\ & V = \left\{ \frac{-18}{7} \right\} & \\\end{align}\)