Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{-7}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-7}\color{blue}{+7-x } & = & 10 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 10 \color{blue}{+7} \\\Leftrightarrow &-16x & = &17\\\Leftrightarrow & \color{red}{-16}x & = &17\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{17}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{16} } & & \\ & V = \left\{ \frac{-17}{16} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{+2}& = & 7 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{+2}\color{blue}{-2-5x } & = & 7 \color{red}{ +5x }\color{blue}{-2-5x } \\\Leftrightarrow & -2x \color{blue}{-5x } & = & 7 \color{blue}{-2} \\\Leftrightarrow &-7x & = &5\\\Leftrightarrow & \color{red}{-7}x & = &5\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{5}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{+8}& = & -4 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{+8}\color{blue}{-8-14x } & = & -4 \color{red}{ +14x }\color{blue}{-8-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & -4 \color{blue}{-8} \\\Leftrightarrow &-25x & = &-12\\\Leftrightarrow & \color{red}{-25}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-12}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{12}{25} } & & \\ & V = \left\{ \frac{12}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{-6}& = & -8 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{-6}\color{blue}{+6+11x } & = & -8 \color{red}{ -11x }\color{blue}{+6+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & -8 \color{blue}{+6} \\\Leftrightarrow &26x & = &-2\\\Leftrightarrow & \color{red}{26}x & = &-2\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{-2}{26} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{+5}& = & -9 \color{red}{ +10x } \\\Leftrightarrow & x \color{red}{+5}\color{blue}{-5-10x } & = & -9 \color{red}{ +10x }\color{blue}{-5-10x } \\\Leftrightarrow & x \color{blue}{-10x } & = & -9 \color{blue}{-5} \\\Leftrightarrow &-9x & = &-14\\\Leftrightarrow & \color{red}{-9}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-14}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{14}{9} } & & \\ & V = \left\{ \frac{14}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{+5}& = & -10 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{+5}\color{blue}{-5-5x } & = & -10 \color{red}{ +5x }\color{blue}{-5-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & -10 \color{blue}{-5} \\\Leftrightarrow &-14x & = &-15\\\Leftrightarrow & \color{red}{-14}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-15}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{15}{14} } & & \\ & V = \left\{ \frac{15}{14} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{+3}& = & 11 \color{red}{ +3x } \\\Leftrightarrow & 8x \color{red}{+3}\color{blue}{-3-3x } & = & 11 \color{red}{ +3x }\color{blue}{-3-3x } \\\Leftrightarrow & 8x \color{blue}{-3x } & = & 11 \color{blue}{-3} \\\Leftrightarrow &5x & = &8\\\Leftrightarrow & \color{red}{5}x & = &8\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{8}{5} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{-11}& = & 8 \color{red}{ -13x } \\\Leftrightarrow & x \color{red}{-11}\color{blue}{+11+13x } & = & 8 \color{red}{ -13x }\color{blue}{+11+13x } \\\Leftrightarrow & x \color{blue}{+13x } & = & 8 \color{blue}{+11} \\\Leftrightarrow &14x & = &19\\\Leftrightarrow & \color{red}{14}x & = &19\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{19}{14} \\\Leftrightarrow & \color{green}{ x = \frac{19}{14} } & & \\ & V = \left\{ \frac{19}{14} \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{+2}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+2}\color{blue}{-2-x } & = & 12 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 12 \color{blue}{-2} \\\Leftrightarrow &-4x & = &10\\\Leftrightarrow & \color{red}{-4}x & = &10\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{10}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{-9}& = & -10 \color{red}{ +10x } \\\Leftrightarrow & 11x \color{red}{-9}\color{blue}{+9-10x } & = & -10 \color{red}{ +10x }\color{blue}{+9-10x } \\\Leftrightarrow & 11x \color{blue}{-10x } & = & -10 \color{blue}{+9} \\\Leftrightarrow &x & = &-1\\\Leftrightarrow & \color{red}{}x & = &-1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -1 \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{+9}& = & 9 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{+9}\color{blue}{-9+7x } & = & 9 \color{red}{ -7x }\color{blue}{-9+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & 9 \color{blue}{-9} \\\Leftrightarrow &11x & = &0\\\Leftrightarrow & \color{red}{11}x & = &0\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{0}{11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{-3}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{-3}\color{blue}{+3-x } & = & 3 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 7x \color{blue}{-x } & = & 3 \color{blue}{+3} \\\Leftrightarrow &6x & = &6\\\Leftrightarrow & \color{red}{6}x & = &6\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{6}{6} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)