Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{+9}& = & -6 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+9}\color{blue}{-9+13x } & = & -6 \color{red}{ -13x }\color{blue}{-9+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -6 \color{blue}{-9} \\\Leftrightarrow &27x & = &-15\\\Leftrightarrow & \color{red}{27}x & = &-15\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-15}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{9} } & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{+14}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+14}\color{blue}{-14-x } & = & -4 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -4 \color{blue}{-14} \\\Leftrightarrow &-9x & = &-18\\\Leftrightarrow & \color{red}{-9}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-18}{-9} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{-15}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-15}\color{blue}{+15-x } & = & -2 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -2 \color{blue}{+15} \\\Leftrightarrow &-10x & = &13\\\Leftrightarrow & \color{red}{-10}x & = &13\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{13}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{10} } & & \\ & V = \left\{ \frac{-13}{10} \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{+2}& = & 14 \color{red}{ -9x } \\\Leftrightarrow & -x \color{red}{+2}\color{blue}{-2+9x } & = & 14 \color{red}{ -9x }\color{blue}{-2+9x } \\\Leftrightarrow & -x \color{blue}{+9x } & = & 14 \color{blue}{-2} \\\Leftrightarrow &8x & = &12\\\Leftrightarrow & \color{red}{8}x & = &12\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{12}{8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{-10}& = & -4 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{-10}\color{blue}{+10-5x } & = & -4 \color{red}{ +5x }\color{blue}{+10-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -4 \color{blue}{+10} \\\Leftrightarrow &7x & = &6\\\Leftrightarrow & \color{red}{7}x & = &6\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{6}{7} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{+15}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+15}\color{blue}{-15-x } & = & 14 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 14 \color{blue}{-15} \\\Leftrightarrow &-9x & = &-1\\\Leftrightarrow & \color{red}{-9}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-1}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{+11}& = & -4 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{+11}\color{blue}{-11-x } & = & -4 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & -4 \color{blue}{-11} \\\Leftrightarrow &8x & = &-15\\\Leftrightarrow & \color{red}{8}x & = &-15\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-15}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{8} } & & \\ & V = \left\{ \frac{-15}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{-5}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-5}\color{blue}{+5-x } & = & -13 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -13 \color{blue}{+5} \\\Leftrightarrow &-15x & = &-8\\\Leftrightarrow & \color{red}{-15}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{8}{15} } & & \\ & V = \left\{ \frac{8}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{+5}& = & 3 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+5}\color{blue}{-5-5x } & = & 3 \color{red}{ +5x }\color{blue}{-5-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & 3 \color{blue}{-5} \\\Leftrightarrow &7x & = &-2\\\Leftrightarrow & \color{red}{7}x & = &-2\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-2}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{-1}& = & -5 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{-1}\color{blue}{+1-11x } & = & -5 \color{red}{ +11x }\color{blue}{+1-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & -5 \color{blue}{+1} \\\Leftrightarrow &-16x & = &-4\\\Leftrightarrow & \color{red}{-16}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-4}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{+5}& = & 15 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+5}\color{blue}{-5-7x } & = & 15 \color{red}{ +7x }\color{blue}{-5-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 15 \color{blue}{-5} \\\Leftrightarrow &-17x & = &10\\\Leftrightarrow & \color{red}{-17}x & = &10\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{10}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{17} } & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{-1}& = & 7 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{-1}\color{blue}{+1-13x } & = & 7 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & 7 \color{blue}{+1} \\\Leftrightarrow &-3x & = &8\\\Leftrightarrow & \color{red}{-3}x & = &8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)