Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 7x \color{red}{+7}& = & 4 \color{red}{ +5x } \\\Leftrightarrow & 7x \color{red}{+7}\color{blue}{-7-5x } & = & 4 \color{red}{ +5x }\color{blue}{-7-5x } \\\Leftrightarrow & 7x \color{blue}{-5x } & = & 4 \color{blue}{-7} \\\Leftrightarrow &2x & = &-3\\\Leftrightarrow & \color{red}{2}x & = &-3\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-3}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{-9}& = & -4 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{-9}\color{blue}{+9-10x } & = & -4 \color{red}{ +10x }\color{blue}{+9-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & -4 \color{blue}{+9} \\\Leftrightarrow &-19x & = &5\\\Leftrightarrow & \color{red}{-19}x & = &5\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{5}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{19} } & & \\ & V = \left\{ \frac{-5}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{+4}& = & 7 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{+4}\color{blue}{-4+12x } & = & 7 \color{red}{ -12x }\color{blue}{-4+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & 7 \color{blue}{-4} \\\Leftrightarrow &25x & = &3\\\Leftrightarrow & \color{red}{25}x & = &3\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{3}{25} \\\Leftrightarrow & \color{green}{ x = \frac{3}{25} } & & \\ & V = \left\{ \frac{3}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{+14}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+14}\color{blue}{-14-x } & = & 1 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 1 \color{blue}{-14} \\\Leftrightarrow &-7x & = &-13\\\Leftrightarrow & \color{red}{-7}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-13}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{13}{7} } & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{+2}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+2}\color{blue}{-2-x } & = & -7 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -7 \color{blue}{-2} \\\Leftrightarrow &-15x & = &-9\\\Leftrightarrow & \color{red}{-15}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-9}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{+3}& = & 9 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{+3}\color{blue}{-3-11x } & = & 9 \color{red}{ +11x }\color{blue}{-3-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & 9 \color{blue}{-3} \\\Leftrightarrow &4x & = &6\\\Leftrightarrow & \color{red}{4}x & = &6\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{6}{4} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{-13}& = & 15 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{-13}\color{blue}{+13+4x } & = & 15 \color{red}{ -4x }\color{blue}{+13+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & 15 \color{blue}{+13} \\\Leftrightarrow &13x & = &28\\\Leftrightarrow & \color{red}{13}x & = &28\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{28}{13} \\\Leftrightarrow & \color{green}{ x = \frac{28}{13} } & & \\ & V = \left\{ \frac{28}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{+5}& = & 13 \color{red}{ +3x } \\\Leftrightarrow & 4x \color{red}{+5}\color{blue}{-5-3x } & = & 13 \color{red}{ +3x }\color{blue}{-5-3x } \\\Leftrightarrow & 4x \color{blue}{-3x } & = & 13 \color{blue}{-5} \\\Leftrightarrow &x & = &8\\\Leftrightarrow & \color{red}{}x & = &8\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 8 \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{-9}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-9}\color{blue}{+9-x } & = & -6 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -6 \color{blue}{+9} \\\Leftrightarrow &-15x & = &3\\\Leftrightarrow & \color{red}{-15}x & = &3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{+13}& = & 1 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+13}\color{blue}{-13+6x } & = & 1 \color{red}{ -6x }\color{blue}{-13+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 1 \color{blue}{-13} \\\Leftrightarrow &19x & = &-12\\\Leftrightarrow & \color{red}{19}x & = &-12\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-12}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{19} } & & \\ & V = \left\{ \frac{-12}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{-5}& = & -12 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{-5}\color{blue}{+5+9x } & = & -12 \color{red}{ -9x }\color{blue}{+5+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & -12 \color{blue}{+5} \\\Leftrightarrow &14x & = &-7\\\Leftrightarrow & \color{red}{14}x & = &-7\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-7}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{-10}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-10}\color{blue}{+10-x } & = & 8 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 8 \color{blue}{+10} \\\Leftrightarrow &-5x & = &18\\\Leftrightarrow & \color{red}{-5}x & = &18\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{18}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{5} } & & \\ & V = \left\{ \frac{-18}{5} \right\} & \\\end{align}\)