Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{+9}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+9}\color{blue}{-9-x } & = & -4 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -4 \color{blue}{-9} \\\Leftrightarrow &-9x & = &-13\\\Leftrightarrow & \color{red}{-9}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-13}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{13}{9} } & & \\ & V = \left\{ \frac{13}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{-5}& = & 14 \color{red}{ -8x } \\\Leftrightarrow & 11x \color{red}{-5}\color{blue}{+5+8x } & = & 14 \color{red}{ -8x }\color{blue}{+5+8x } \\\Leftrightarrow & 11x \color{blue}{+8x } & = & 14 \color{blue}{+5} \\\Leftrightarrow &19x & = &19\\\Leftrightarrow & \color{red}{19}x & = &19\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{19}{19} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{+8}& = & 12 \color{red}{ +9x } \\\Leftrightarrow & 2x \color{red}{+8}\color{blue}{-8-9x } & = & 12 \color{red}{ +9x }\color{blue}{-8-9x } \\\Leftrightarrow & 2x \color{blue}{-9x } & = & 12 \color{blue}{-8} \\\Leftrightarrow &-7x & = &4\\\Leftrightarrow & \color{red}{-7}x & = &4\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{4}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{-11}& = & -6 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{-11}\color{blue}{+11-11x } & = & -6 \color{red}{ +11x }\color{blue}{+11-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & -6 \color{blue}{+11} \\\Leftrightarrow &x & = &5\\\Leftrightarrow & \color{red}{}x & = &5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 5 \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{-10}& = & -4 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{-10}\color{blue}{+10-x } & = & -4 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & -4 \color{blue}{+10} \\\Leftrightarrow &8x & = &6\\\Leftrightarrow & \color{red}{8}x & = &6\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{6}{8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{-5}& = & 8 \color{red}{ +3x } \\\Leftrightarrow & 4x \color{red}{-5}\color{blue}{+5-3x } & = & 8 \color{red}{ +3x }\color{blue}{+5-3x } \\\Leftrightarrow & 4x \color{blue}{-3x } & = & 8 \color{blue}{+5} \\\Leftrightarrow &x & = &13\\\Leftrightarrow & \color{red}{}x & = &13\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 13 \\\Leftrightarrow & \color{green}{ x = 13 } & & \\ & V = \left\{ 13 \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{-3}& = & -11 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{-3}\color{blue}{+3-7x } & = & -11 \color{red}{ +7x }\color{blue}{+3-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & -11 \color{blue}{+3} \\\Leftrightarrow &-16x & = &-8\\\Leftrightarrow & \color{red}{-16}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-8}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{+14}& = & 12 \color{red}{ +10x } \\\Leftrightarrow & 11x \color{red}{+14}\color{blue}{-14-10x } & = & 12 \color{red}{ +10x }\color{blue}{-14-10x } \\\Leftrightarrow & 11x \color{blue}{-10x } & = & 12 \color{blue}{-14} \\\Leftrightarrow &x & = &-2\\\Leftrightarrow & \color{red}{}x & = &-2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -2 \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{+7}& = & 3 \color{red}{ +3x } \\\Leftrightarrow & 13x \color{red}{+7}\color{blue}{-7-3x } & = & 3 \color{red}{ +3x }\color{blue}{-7-3x } \\\Leftrightarrow & 13x \color{blue}{-3x } & = & 3 \color{blue}{-7} \\\Leftrightarrow &10x & = &-4\\\Leftrightarrow & \color{red}{10}x & = &-4\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-4}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{-11}& = & 13 \color{red}{ +10x } \\\Leftrightarrow & 7x \color{red}{-11}\color{blue}{+11-10x } & = & 13 \color{red}{ +10x }\color{blue}{+11-10x } \\\Leftrightarrow & 7x \color{blue}{-10x } & = & 13 \color{blue}{+11} \\\Leftrightarrow &-3x & = &24\\\Leftrightarrow & \color{red}{-3}x & = &24\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{24}{-3} \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{+2}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{+2}\color{blue}{-2-7x } & = & 11 \color{red}{ +7x }\color{blue}{-2-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & 11 \color{blue}{-2} \\\Leftrightarrow &8x & = &9\\\Leftrightarrow & \color{red}{8}x & = &9\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{9}{8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{8} } & & \\ & V = \left\{ \frac{9}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{+1}& = & -2 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{+1}\color{blue}{-1+10x } & = & -2 \color{red}{ -10x }\color{blue}{-1+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & -2 \color{blue}{-1} \\\Leftrightarrow &17x & = &-3\\\Leftrightarrow & \color{red}{17}x & = &-3\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-3}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{17} } & & \\ & V = \left\{ \frac{-3}{17} \right\} & \\\end{align}\)