Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{+2}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+2}\color{blue}{-2-x } & = & -13 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -13 \color{blue}{-2} \\\Leftrightarrow &-9x & = &-15\\\Leftrightarrow & \color{red}{-9}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-15}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{+12}& = & -15 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{+12}\color{blue}{-12-10x } & = & -15 \color{red}{ +10x }\color{blue}{-12-10x } \\\Leftrightarrow & 9x \color{blue}{-10x } & = & -15 \color{blue}{-12} \\\Leftrightarrow &-x & = &-27\\\Leftrightarrow & \color{red}{-}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-27}{-1} \\\Leftrightarrow & \color{green}{ x = 27 } & & \\ & V = \left\{ 27 \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{-7}& = & 12 \color{red}{ -10x } \\\Leftrightarrow & -x \color{red}{-7}\color{blue}{+7+10x } & = & 12 \color{red}{ -10x }\color{blue}{+7+10x } \\\Leftrightarrow & -x \color{blue}{+10x } & = & 12 \color{blue}{+7} \\\Leftrightarrow &9x & = &19\\\Leftrightarrow & \color{red}{9}x & = &19\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{19}{9} \\\Leftrightarrow & \color{green}{ x = \frac{19}{9} } & & \\ & V = \left\{ \frac{19}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{+3}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+3}\color{blue}{-3-x } & = & -6 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -6 \color{blue}{-3} \\\Leftrightarrow &-14x & = &-9\\\Leftrightarrow & \color{red}{-14}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-9}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{9}{14} } & & \\ & V = \left\{ \frac{9}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{-6}& = & -10 \color{red}{ -8x } \\\Leftrightarrow & x \color{red}{-6}\color{blue}{+6+8x } & = & -10 \color{red}{ -8x }\color{blue}{+6+8x } \\\Leftrightarrow & x \color{blue}{+8x } & = & -10 \color{blue}{+6} \\\Leftrightarrow &9x & = &-4\\\Leftrightarrow & \color{red}{9}x & = &-4\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-4}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{9} } & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & -7x \color{red}{-12}& = & -1 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{-12}\color{blue}{+12-8x } & = & -1 \color{red}{ +8x }\color{blue}{+12-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & -1 \color{blue}{+12} \\\Leftrightarrow &-15x & = &11\\\Leftrightarrow & \color{red}{-15}x & = &11\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{11}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{15} } & & \\ & V = \left\{ \frac{-11}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{+11}& = & -9 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{+11}\color{blue}{-11-10x } & = & -9 \color{red}{ +10x }\color{blue}{-11-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & -9 \color{blue}{-11} \\\Leftrightarrow &-13x & = &-20\\\Leftrightarrow & \color{red}{-13}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-20}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{20}{13} } & & \\ & V = \left\{ \frac{20}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{+2}& = & -5 \color{red}{ +13x } \\\Leftrightarrow & 4x \color{red}{+2}\color{blue}{-2-13x } & = & -5 \color{red}{ +13x }\color{blue}{-2-13x } \\\Leftrightarrow & 4x \color{blue}{-13x } & = & -5 \color{blue}{-2} \\\Leftrightarrow &-9x & = &-7\\\Leftrightarrow & \color{red}{-9}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{9} } & & \\ & V = \left\{ \frac{7}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{-7}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-7}\color{blue}{+7-x } & = & -7 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -7 \color{blue}{+7} \\\Leftrightarrow &-11x & = &0\\\Leftrightarrow & \color{red}{-11}x & = &0\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{0}{-11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{+6}& = & -6 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{+6}\color{blue}{-6-9x } & = & -6 \color{red}{ +9x }\color{blue}{-6-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & -6 \color{blue}{-6} \\\Leftrightarrow &-x & = &-12\\\Leftrightarrow & \color{red}{-}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-12}{-1} \\\Leftrightarrow & \color{green}{ x = 12 } & & \\ & V = \left\{ 12 \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{-11}& = & -11 \color{red}{ +6x } \\\Leftrightarrow & 7x \color{red}{-11}\color{blue}{+11-6x } & = & -11 \color{red}{ +6x }\color{blue}{+11-6x } \\\Leftrightarrow & 7x \color{blue}{-6x } & = & -11 \color{blue}{+11} \\\Leftrightarrow &x & = &0\\\Leftrightarrow & \color{red}{}x & = &0\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 0 \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{+1}& = & 5 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{+1}\color{blue}{-1+10x } & = & 5 \color{red}{ -10x }\color{blue}{-1+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & 5 \color{blue}{-1} \\\Leftrightarrow &21x & = &4\\\Leftrightarrow & \color{red}{21}x & = &4\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{4}{21} \\\Leftrightarrow & \color{green}{ x = \frac{4}{21} } & & \\ & V = \left\{ \frac{4}{21} \right\} & \\\end{align}\)