Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{-6}& = & -5 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{-6}\color{blue}{+6-4x } & = & -5 \color{red}{ +4x }\color{blue}{+6-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & -5 \color{blue}{+6} \\\Leftrightarrow &-11x & = &1\\\Leftrightarrow & \color{red}{-11}x & = &1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{-4}& = & -7 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{-4}\color{blue}{+4-3x } & = & -7 \color{red}{ +3x }\color{blue}{+4-3x } \\\Leftrightarrow & 2x \color{blue}{-3x } & = & -7 \color{blue}{+4} \\\Leftrightarrow &-x & = &-3\\\Leftrightarrow & \color{red}{-}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-3}{-1} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{+6}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+6}\color{blue}{-6-x } & = & -7 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -7 \color{blue}{-6} \\\Leftrightarrow &-12x & = &-13\\\Leftrightarrow & \color{red}{-12}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-13}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{13}{12} } & & \\ & V = \left\{ \frac{13}{12} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{+15}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+15}\color{blue}{-15-x } & = & 10 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 10 \color{blue}{-15} \\\Leftrightarrow &-12x & = &-5\\\Leftrightarrow & \color{red}{-12}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-5}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{12} } & & \\ & V = \left\{ \frac{5}{12} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{+2}& = & -13 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+2}\color{blue}{-2-9x } & = & -13 \color{red}{ +9x }\color{blue}{-2-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -13 \color{blue}{-2} \\\Leftrightarrow &-17x & = &-15\\\Leftrightarrow & \color{red}{-17}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-15}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{15}{17} } & & \\ & V = \left\{ \frac{15}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{-11}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-11}\color{blue}{+11-x } & = & -12 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -12 \color{blue}{+11} \\\Leftrightarrow &-11x & = &-1\\\Leftrightarrow & \color{red}{-11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{-1}& = & -13 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{-1}\color{blue}{+1-6x } & = & -13 \color{red}{ +6x }\color{blue}{+1-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & -13 \color{blue}{+1} \\\Leftrightarrow &-11x & = &-12\\\Leftrightarrow & \color{red}{-11}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-12}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{12}{11} } & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{-15}& = & 9 \color{red}{ +7x } \\\Leftrightarrow & -2x \color{red}{-15}\color{blue}{+15-7x } & = & 9 \color{red}{ +7x }\color{blue}{+15-7x } \\\Leftrightarrow & -2x \color{blue}{-7x } & = & 9 \color{blue}{+15} \\\Leftrightarrow &-9x & = &24\\\Leftrightarrow & \color{red}{-9}x & = &24\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{24}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{+1}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+1}\color{blue}{-1-7x } & = & -7 \color{red}{ +7x }\color{blue}{-1-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -7 \color{blue}{-1} \\\Leftrightarrow &-17x & = &-8\\\Leftrightarrow & \color{red}{-17}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-8}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{8}{17} } & & \\ & V = \left\{ \frac{8}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{-14}& = & 2 \color{red}{ +4x } \\\Leftrightarrow & 5x \color{red}{-14}\color{blue}{+14-4x } & = & 2 \color{red}{ +4x }\color{blue}{+14-4x } \\\Leftrightarrow & 5x \color{blue}{-4x } & = & 2 \color{blue}{+14} \\\Leftrightarrow &x & = &16\\\Leftrightarrow & \color{red}{}x & = &16\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 16 \\\Leftrightarrow & \color{green}{ x = 16 } & & \\ & V = \left\{ 16 \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{+11}& = & -2 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{+11}\color{blue}{-11-14x } & = & -2 \color{red}{ +14x }\color{blue}{-11-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -2 \color{blue}{-11} \\\Leftrightarrow &-23x & = &-13\\\Leftrightarrow & \color{red}{-23}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-13}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{13}{23} } & & \\ & V = \left\{ \frac{13}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{-5}& = & 7 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{-5}\color{blue}{+5+3x } & = & 7 \color{red}{ -3x }\color{blue}{+5+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & 7 \color{blue}{+5} \\\Leftrightarrow &10x & = &12\\\Leftrightarrow & \color{red}{10}x & = &12\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{12}{10} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)