Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{+11}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+11}\color{blue}{-11-x } & = & -3 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -3 \color{blue}{-11} \\\Leftrightarrow &-9x & = &-14\\\Leftrightarrow & \color{red}{-9}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-14}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{14}{9} } & & \\ & V = \left\{ \frac{14}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{+14}& = & -6 \color{red}{ +15x } \\\Leftrightarrow & -x \color{red}{+14}\color{blue}{-14-15x } & = & -6 \color{red}{ +15x }\color{blue}{-14-15x } \\\Leftrightarrow & -x \color{blue}{-15x } & = & -6 \color{blue}{-14} \\\Leftrightarrow &-16x & = &-20\\\Leftrightarrow & \color{red}{-16}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-20}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{-10}& = & 7 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{-10}\color{blue}{+10-11x } & = & 7 \color{red}{ +11x }\color{blue}{+10-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & 7 \color{blue}{+10} \\\Leftrightarrow &-18x & = &17\\\Leftrightarrow & \color{red}{-18}x & = &17\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{17}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{18} } & & \\ & V = \left\{ \frac{-17}{18} \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{+12}& = & 7 \color{red}{ +8x } \\\Leftrightarrow & -x \color{red}{+12}\color{blue}{-12-8x } & = & 7 \color{red}{ +8x }\color{blue}{-12-8x } \\\Leftrightarrow & -x \color{blue}{-8x } & = & 7 \color{blue}{-12} \\\Leftrightarrow &-9x & = &-5\\\Leftrightarrow & \color{red}{-9}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-5}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{9} } & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{+10}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+10}\color{blue}{-10-x } & = & -6 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -6 \color{blue}{-10} \\\Leftrightarrow &-4x & = &-16\\\Leftrightarrow & \color{red}{-4}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-16}{-4} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{-2}& = & 1 \color{red}{ +5x } \\\Leftrightarrow & 13x \color{red}{-2}\color{blue}{+2-5x } & = & 1 \color{red}{ +5x }\color{blue}{+2-5x } \\\Leftrightarrow & 13x \color{blue}{-5x } & = & 1 \color{blue}{+2} \\\Leftrightarrow &8x & = &3\\\Leftrightarrow & \color{red}{8}x & = &3\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{3}{8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{-5}& = & -6 \color{red}{ +8x } \\\Leftrightarrow & x \color{red}{-5}\color{blue}{+5-8x } & = & -6 \color{red}{ +8x }\color{blue}{+5-8x } \\\Leftrightarrow & x \color{blue}{-8x } & = & -6 \color{blue}{+5} \\\Leftrightarrow &-7x & = &-1\\\Leftrightarrow & \color{red}{-7}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{+10}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+10}\color{blue}{-10-x } & = & 9 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 9 \color{blue}{-10} \\\Leftrightarrow &-15x & = &-1\\\Leftrightarrow & \color{red}{-15}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{15} } & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{-14}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-14}\color{blue}{+14-x } & = & -2 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -2 \color{blue}{+14} \\\Leftrightarrow &-4x & = &12\\\Leftrightarrow & \color{red}{-4}x & = &12\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{12}{-4} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{+10}& = & 2 \color{red}{ +13x } \\\Leftrightarrow & 12x \color{red}{+10}\color{blue}{-10-13x } & = & 2 \color{red}{ +13x }\color{blue}{-10-13x } \\\Leftrightarrow & 12x \color{blue}{-13x } & = & 2 \color{blue}{-10} \\\Leftrightarrow &-x & = &-8\\\Leftrightarrow & \color{red}{-}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-8}{-1} \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{+15}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+15}\color{blue}{-15-x } & = & -6 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -6 \color{blue}{-15} \\\Leftrightarrow &13x & = &-21\\\Leftrightarrow & \color{red}{13}x & = &-21\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-21}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{13} } & & \\ & V = \left\{ \frac{-21}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{-7}& = & 15 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-7}\color{blue}{+7-7x } & = & 15 \color{red}{ +7x }\color{blue}{+7-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 15 \color{blue}{+7} \\\Leftrightarrow &-17x & = &22\\\Leftrightarrow & \color{red}{-17}x & = &22\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{22}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{17} } & & \\ & V = \left\{ \frac{-22}{17} \right\} & \\\end{align}\)