Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{-15}& = & -14 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{-15}\color{blue}{+15-7x } & = & -14 \color{red}{ +7x }\color{blue}{+15-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & -14 \color{blue}{+15} \\\Leftrightarrow &-16x & = &1\\\Leftrightarrow & \color{red}{-16}x & = &1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{16} } & & \\ & V = \left\{ \frac{-1}{16} \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{+3}& = & 7 \color{red}{ +13x } \\\Leftrightarrow & x \color{red}{+3}\color{blue}{-3-13x } & = & 7 \color{red}{ +13x }\color{blue}{-3-13x } \\\Leftrightarrow & x \color{blue}{-13x } & = & 7 \color{blue}{-3} \\\Leftrightarrow &-12x & = &4\\\Leftrightarrow & \color{red}{-12}x & = &4\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{4}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{-3}& = & 14 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{-3}\color{blue}{+3+7x } & = & 14 \color{red}{ -7x }\color{blue}{+3+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & 14 \color{blue}{+3} \\\Leftrightarrow &22x & = &17\\\Leftrightarrow & \color{red}{22}x & = &17\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{17}{22} \\\Leftrightarrow & \color{green}{ x = \frac{17}{22} } & & \\ & V = \left\{ \frac{17}{22} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{+8}& = & -1 \color{red}{ +4x } \\\Leftrightarrow & 15x \color{red}{+8}\color{blue}{-8-4x } & = & -1 \color{red}{ +4x }\color{blue}{-8-4x } \\\Leftrightarrow & 15x \color{blue}{-4x } & = & -1 \color{blue}{-8} \\\Leftrightarrow &11x & = &-9\\\Leftrightarrow & \color{red}{11}x & = &-9\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-9}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{11} } & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{-12}& = & -7 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-12}\color{blue}{+12+8x } & = & -7 \color{red}{ -8x }\color{blue}{+12+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & -7 \color{blue}{+12} \\\Leftrightarrow &11x & = &5\\\Leftrightarrow & \color{red}{11}x & = &5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{-14}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-14}\color{blue}{+14-x } & = & -4 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -4 \color{blue}{+14} \\\Leftrightarrow &-5x & = &10\\\Leftrightarrow & \color{red}{-5}x & = &10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{10}{-5} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{+14}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+14}\color{blue}{-14-x } & = & -6 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -6 \color{blue}{-14} \\\Leftrightarrow &-8x & = &-20\\\Leftrightarrow & \color{red}{-8}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-20}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{-12}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-12}\color{blue}{+12-x } & = & -5 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -5 \color{blue}{+12} \\\Leftrightarrow &-10x & = &7\\\Leftrightarrow & \color{red}{-10}x & = &7\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{7}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{10} } & & \\ & V = \left\{ \frac{-7}{10} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{+7}& = & -5 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+7}\color{blue}{-7+11x } & = & -5 \color{red}{ -11x }\color{blue}{-7+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & -5 \color{blue}{-7} \\\Leftrightarrow &15x & = &-12\\\Leftrightarrow & \color{red}{15}x & = &-12\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-12}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{+9}& = & -14 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{+9}\color{blue}{-9-14x } & = & -14 \color{red}{ +14x }\color{blue}{-9-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & -14 \color{blue}{-9} \\\Leftrightarrow &-27x & = &-23\\\Leftrightarrow & \color{red}{-27}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{-23}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{23}{27} } & & \\ & V = \left\{ \frac{23}{27} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{-15}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-15}\color{blue}{+15-x } & = & 3 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 3 \color{blue}{+15} \\\Leftrightarrow &-7x & = &18\\\Leftrightarrow & \color{red}{-7}x & = &18\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{18}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{7} } & & \\ & V = \left\{ \frac{-18}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{-11}& = & -14 \color{red}{ -10x } \\\Leftrightarrow & -x \color{red}{-11}\color{blue}{+11+10x } & = & -14 \color{red}{ -10x }\color{blue}{+11+10x } \\\Leftrightarrow & -x \color{blue}{+10x } & = & -14 \color{blue}{+11} \\\Leftrightarrow &9x & = &-3\\\Leftrightarrow & \color{red}{9}x & = &-3\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-3}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)