Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{-6}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-6}\color{blue}{+6-x } & = & -14 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -14 \color{blue}{+6} \\\Leftrightarrow &-8x & = &-8\\\Leftrightarrow & \color{red}{-8}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-8}{-8} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{+2}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+2}\color{blue}{-2-x } & = & -14 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -14 \color{blue}{-2} \\\Leftrightarrow &-8x & = &-16\\\Leftrightarrow & \color{red}{-8}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-16}{-8} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{-8}& = & -2 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{-8}\color{blue}{+8-5x } & = & -2 \color{red}{ +5x }\color{blue}{+8-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & -2 \color{blue}{+8} \\\Leftrightarrow &x & = &6\\\Leftrightarrow & \color{red}{}x & = &6\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 6 \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{+10}& = & 2 \color{red}{ -5x } \\\Leftrightarrow & 8x \color{red}{+10}\color{blue}{-10+5x } & = & 2 \color{red}{ -5x }\color{blue}{-10+5x } \\\Leftrightarrow & 8x \color{blue}{+5x } & = & 2 \color{blue}{-10} \\\Leftrightarrow &13x & = &-8\\\Leftrightarrow & \color{red}{13}x & = &-8\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-8}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{13} } & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{+4}& = & -2 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{+4}\color{blue}{-4-4x } & = & -2 \color{red}{ +4x }\color{blue}{-4-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & -2 \color{blue}{-4} \\\Leftrightarrow &-7x & = &-6\\\Leftrightarrow & \color{red}{-7}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-6}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{+8}& = & 9 \color{red}{ +11x } \\\Leftrightarrow & 10x \color{red}{+8}\color{blue}{-8-11x } & = & 9 \color{red}{ +11x }\color{blue}{-8-11x } \\\Leftrightarrow & 10x \color{blue}{-11x } & = & 9 \color{blue}{-8} \\\Leftrightarrow &-x & = &1\\\Leftrightarrow & \color{red}{-}x & = &1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{1}{-1} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{+5}& = & -13 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{+5}\color{blue}{-5-8x } & = & -13 \color{red}{ +8x }\color{blue}{-5-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & -13 \color{blue}{-5} \\\Leftrightarrow &-23x & = &-18\\\Leftrightarrow & \color{red}{-23}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-18}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{18}{23} } & & \\ & V = \left\{ \frac{18}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{+12}& = & -14 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+12}\color{blue}{-12+11x } & = & -14 \color{red}{ -11x }\color{blue}{-12+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -14 \color{blue}{-12} \\\Leftrightarrow &17x & = &-26\\\Leftrightarrow & \color{red}{17}x & = &-26\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-26}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{17} } & & \\ & V = \left\{ \frac{-26}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{-6}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-6}\color{blue}{+6-x } & = & 6 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 6 \color{blue}{+6} \\\Leftrightarrow &-5x & = &12\\\Leftrightarrow & \color{red}{-5}x & = &12\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{12}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{5} } & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 15x \color{red}{-6}& = & 7 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{-6}\color{blue}{+6+11x } & = & 7 \color{red}{ -11x }\color{blue}{+6+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & 7 \color{blue}{+6} \\\Leftrightarrow &26x & = &13\\\Leftrightarrow & \color{red}{26}x & = &13\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{13}{26} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{+7}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+7}\color{blue}{-7-x } & = & 10 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 10 \color{blue}{-7} \\\Leftrightarrow &-7x & = &3\\\Leftrightarrow & \color{red}{-7}x & = &3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{+7}& = & 9 \color{red}{ +4x } \\\Leftrightarrow & 5x \color{red}{+7}\color{blue}{-7-4x } & = & 9 \color{red}{ +4x }\color{blue}{-7-4x } \\\Leftrightarrow & 5x \color{blue}{-4x } & = & 9 \color{blue}{-7} \\\Leftrightarrow &x & = &2\\\Leftrightarrow & \color{red}{}x & = &2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 2 \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)