Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{+4}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+4}\color{blue}{-4-x } & = & -6 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -6 \color{blue}{-4} \\\Leftrightarrow &-15x & = &-10\\\Leftrightarrow & \color{red}{-15}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-10}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{+8}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & 3x \color{red}{+8}\color{blue}{-8-13x } & = & -10 \color{red}{ +13x }\color{blue}{-8-13x } \\\Leftrightarrow & 3x \color{blue}{-13x } & = & -10 \color{blue}{-8} \\\Leftrightarrow &-10x & = &-18\\\Leftrightarrow & \color{red}{-10}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-18}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{-11}& = & 6 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-11}\color{blue}{+11-9x } & = & 6 \color{red}{ +9x }\color{blue}{+11-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 6 \color{blue}{+11} \\\Leftrightarrow &-17x & = &17\\\Leftrightarrow & \color{red}{-17}x & = &17\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{17}{-17} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{+2}& = & -4 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{+2}\color{blue}{-2-9x } & = & -4 \color{red}{ +9x }\color{blue}{-2-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & -4 \color{blue}{-2} \\\Leftrightarrow &-x & = &-6\\\Leftrightarrow & \color{red}{-}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-6}{-1} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{-1}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-1}\color{blue}{+1-x } & = & 4 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 4 \color{blue}{+1} \\\Leftrightarrow &-15x & = &5\\\Leftrightarrow & \color{red}{-15}x & = &5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{-6}& = & 7 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{-6}\color{blue}{+6+10x } & = & 7 \color{red}{ -10x }\color{blue}{+6+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & 7 \color{blue}{+6} \\\Leftrightarrow &17x & = &13\\\Leftrightarrow & \color{red}{17}x & = &13\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{13}{17} \\\Leftrightarrow & \color{green}{ x = \frac{13}{17} } & & \\ & V = \left\{ \frac{13}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{-11}& = & -8 \color{red}{ +4x } \\\Leftrightarrow & 7x \color{red}{-11}\color{blue}{+11-4x } & = & -8 \color{red}{ +4x }\color{blue}{+11-4x } \\\Leftrightarrow & 7x \color{blue}{-4x } & = & -8 \color{blue}{+11} \\\Leftrightarrow &3x & = &3\\\Leftrightarrow & \color{red}{3}x & = &3\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{3}{3} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{+4}& = & -5 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+4}\color{blue}{-4+13x } & = & -5 \color{red}{ -13x }\color{blue}{-4+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -5 \color{blue}{-4} \\\Leftrightarrow &23x & = &-9\\\Leftrightarrow & \color{red}{23}x & = &-9\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-9}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{23} } & & \\ & V = \left\{ \frac{-9}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{-14}& = & 1 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{-14}\color{blue}{+14-8x } & = & 1 \color{red}{ +8x }\color{blue}{+14-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & 1 \color{blue}{+14} \\\Leftrightarrow &-15x & = &15\\\Leftrightarrow & \color{red}{-15}x & = &15\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{15}{-15} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{+13}& = & 5 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{+13}\color{blue}{-13-11x } & = & 5 \color{red}{ +11x }\color{blue}{-13-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & 5 \color{blue}{-13} \\\Leftrightarrow &-18x & = &-8\\\Leftrightarrow & \color{red}{-18}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{-8}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{4}{9} } & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{+11}& = & -14 \color{red}{ +13x } \\\Leftrightarrow & 8x \color{red}{+11}\color{blue}{-11-13x } & = & -14 \color{red}{ +13x }\color{blue}{-11-13x } \\\Leftrightarrow & 8x \color{blue}{-13x } & = & -14 \color{blue}{-11} \\\Leftrightarrow &-5x & = &-25\\\Leftrightarrow & \color{red}{-5}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-25}{-5} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{+14}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+14}\color{blue}{-14-x } & = & -6 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -6 \color{blue}{-14} \\\Leftrightarrow &-11x & = &-20\\\Leftrightarrow & \color{red}{-11}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-20}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{20}{11} } & & \\ & V = \left\{ \frac{20}{11} \right\} & \\\end{align}\)