Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{-13}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-13}\color{blue}{+13-x } & = & -8 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -8 \color{blue}{+13} \\\Leftrightarrow &-14x & = &5\\\Leftrightarrow & \color{red}{-14}x & = &5\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{5}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{14} } & & \\ & V = \left\{ \frac{-5}{14} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{+6}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+6}\color{blue}{-6-x } & = & -9 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -9 \color{blue}{-6} \\\Leftrightarrow &-9x & = &-15\\\Leftrightarrow & \color{red}{-9}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-15}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{-3}& = & -4 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-3}\color{blue}{+3-13x } & = & -4 \color{red}{ +13x }\color{blue}{+3-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -4 \color{blue}{+3} \\\Leftrightarrow &-25x & = &-1\\\Leftrightarrow & \color{red}{-25}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-1}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{1}{25} } & & \\ & V = \left\{ \frac{1}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{+3}& = & -14 \color{red}{ +2x } \\\Leftrightarrow & -x \color{red}{+3}\color{blue}{-3-2x } & = & -14 \color{red}{ +2x }\color{blue}{-3-2x } \\\Leftrightarrow & -x \color{blue}{-2x } & = & -14 \color{blue}{-3} \\\Leftrightarrow &-3x & = &-17\\\Leftrightarrow & \color{red}{-3}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-17}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{17}{3} } & & \\ & V = \left\{ \frac{17}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{+2}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+2}\color{blue}{-2-x } & = & 6 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & 6 \color{blue}{-2} \\\Leftrightarrow &9x & = &4\\\Leftrightarrow & \color{red}{9}x & = &4\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{4}{9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{9} } & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{-10}& = & -11 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{-10}\color{blue}{+10+9x } & = & -11 \color{red}{ -9x }\color{blue}{+10+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & -11 \color{blue}{+10} \\\Leftrightarrow &14x & = &-1\\\Leftrightarrow & \color{red}{14}x & = &-1\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-1}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{14} } & & \\ & V = \left\{ \frac{-1}{14} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{-11}& = & 4 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{-11}\color{blue}{+11-11x } & = & 4 \color{red}{ +11x }\color{blue}{+11-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & 4 \color{blue}{+11} \\\Leftrightarrow &4x & = &15\\\Leftrightarrow & \color{red}{4}x & = &15\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{15}{4} \\\Leftrightarrow & \color{green}{ x = \frac{15}{4} } & & \\ & V = \left\{ \frac{15}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{+6}& = & 9 \color{red}{ +5x } \\\Leftrightarrow & 13x \color{red}{+6}\color{blue}{-6-5x } & = & 9 \color{red}{ +5x }\color{blue}{-6-5x } \\\Leftrightarrow & 13x \color{blue}{-5x } & = & 9 \color{blue}{-6} \\\Leftrightarrow &8x & = &3\\\Leftrightarrow & \color{red}{8}x & = &3\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{3}{8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{-7}& = & 9 \color{red}{ +12x } \\\Leftrightarrow & x \color{red}{-7}\color{blue}{+7-12x } & = & 9 \color{red}{ +12x }\color{blue}{+7-12x } \\\Leftrightarrow & x \color{blue}{-12x } & = & 9 \color{blue}{+7} \\\Leftrightarrow &-11x & = &16\\\Leftrightarrow & \color{red}{-11}x & = &16\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{16}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{11} } & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{-15}& = & 10 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{-15}\color{blue}{+15-3x } & = & 10 \color{red}{ +3x }\color{blue}{+15-3x } \\\Leftrightarrow & 2x \color{blue}{-3x } & = & 10 \color{blue}{+15} \\\Leftrightarrow &-x & = &25\\\Leftrightarrow & \color{red}{-}x & = &25\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{25}{-1} \\\Leftrightarrow & \color{green}{ x = -25 } & & \\ & V = \left\{ -25 \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{-1}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-1}\color{blue}{+1-x } & = & -5 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -5 \color{blue}{+1} \\\Leftrightarrow &-15x & = &-4\\\Leftrightarrow & \color{red}{-15}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{15} } & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{-11}& = & -7 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{-11}\color{blue}{+11+11x } & = & -7 \color{red}{ -11x }\color{blue}{+11+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & -7 \color{blue}{+11} \\\Leftrightarrow &26x & = &4\\\Leftrightarrow & \color{red}{26}x & = &4\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{4}{26} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)