Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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