Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{+6}& = & 1 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{+6}\color{blue}{-6-11x } & = & 1 \color{red}{ +11x }\color{blue}{-6-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & 1 \color{blue}{-6} \\\Leftrightarrow &4x & = &-5\\\Leftrightarrow & \color{red}{4}x & = &-5\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-5}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{-5}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-5}\color{blue}{+5-x } & = & -14 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -14 \color{blue}{+5} \\\Leftrightarrow &-10x & = &-9\\\Leftrightarrow & \color{red}{-10}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-9}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{9}{10} } & & \\ & V = \left\{ \frac{9}{10} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{+3}& = & -14 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{+3}\color{blue}{-3+9x } & = & -14 \color{red}{ -9x }\color{blue}{-3+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & -14 \color{blue}{-3} \\\Leftrightarrow &14x & = &-17\\\Leftrightarrow & \color{red}{14}x & = &-17\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-17}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{14} } & & \\ & V = \left\{ \frac{-17}{14} \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{-6}& = & -6 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{-6}\color{blue}{+6+7x } & = & -6 \color{red}{ -7x }\color{blue}{+6+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & -6 \color{blue}{+6} \\\Leftrightarrow &19x & = &0\\\Leftrightarrow & \color{red}{19}x & = &0\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{0}{19} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{+11}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+11}\color{blue}{-11-x } & = & 15 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 15 \color{blue}{-11} \\\Leftrightarrow &-14x & = &4\\\Leftrightarrow & \color{red}{-14}x & = &4\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{4}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{-11}& = & 12 \color{red}{ +8x } \\\Leftrightarrow & -13x \color{red}{-11}\color{blue}{+11-8x } & = & 12 \color{red}{ +8x }\color{blue}{+11-8x } \\\Leftrightarrow & -13x \color{blue}{-8x } & = & 12 \color{blue}{+11} \\\Leftrightarrow &-21x & = &23\\\Leftrightarrow & \color{red}{-21}x & = &23\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{23}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{21} } & & \\ & V = \left\{ \frac{-23}{21} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{+2}& = & 15 \color{red}{ +7x } \\\Leftrightarrow & -2x \color{red}{+2}\color{blue}{-2-7x } & = & 15 \color{red}{ +7x }\color{blue}{-2-7x } \\\Leftrightarrow & -2x \color{blue}{-7x } & = & 15 \color{blue}{-2} \\\Leftrightarrow &-9x & = &13\\\Leftrightarrow & \color{red}{-9}x & = &13\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{13}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{9} } & & \\ & V = \left\{ \frac{-13}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{+9}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+9}\color{blue}{-9-x } & = & -11 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -11 \color{blue}{-9} \\\Leftrightarrow &-8x & = &-20\\\Leftrightarrow & \color{red}{-8}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-20}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{+1}& = & -4 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+1}\color{blue}{-1+6x } & = & -4 \color{red}{ -6x }\color{blue}{-1+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -4 \color{blue}{-1} \\\Leftrightarrow &19x & = &-5\\\Leftrightarrow & \color{red}{19}x & = &-5\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-5}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{19} } & & \\ & V = \left\{ \frac{-5}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{+6}& = & 13 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{+6}\color{blue}{-6-5x } & = & 13 \color{red}{ +5x }\color{blue}{-6-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & 13 \color{blue}{-6} \\\Leftrightarrow &-17x & = &7\\\Leftrightarrow & \color{red}{-17}x & = &7\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{7}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{17} } & & \\ & V = \left\{ \frac{-7}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{+7}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+7}\color{blue}{-7-x } & = & 5 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 5 \color{blue}{-7} \\\Leftrightarrow &-6x & = &-2\\\Leftrightarrow & \color{red}{-6}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{+6}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+6}\color{blue}{-6-x } & = & -11 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -11 \color{blue}{-6} \\\Leftrightarrow &-13x & = &-17\\\Leftrightarrow & \color{red}{-13}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-17}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{17}{13} } & & \\ & V = \left\{ \frac{17}{13} \right\} & \\\end{align}\)