Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{-9}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-9}\color{blue}{+9-x } & = & 6 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 6 \color{blue}{+9} \\\Leftrightarrow &-16x & = &15\\\Leftrightarrow & \color{red}{-16}x & = &15\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{15}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{16} } & & \\ & V = \left\{ \frac{-15}{16} \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{-2}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{-2}\color{blue}{+2-x } & = & 3 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & 7x \color{blue}{-x } & = & 3 \color{blue}{+2} \\\Leftrightarrow &6x & = &5\\\Leftrightarrow & \color{red}{6}x & = &5\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{5}{6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{-3}& = & -3 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{-3}\color{blue}{+3+2x } & = & -3 \color{red}{ -2x }\color{blue}{+3+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & -3 \color{blue}{+3} \\\Leftrightarrow &5x & = &0\\\Leftrightarrow & \color{red}{5}x & = &0\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{0}{5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{-7}& = & 2 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-7}\color{blue}{+7+7x } & = & 2 \color{red}{ -7x }\color{blue}{+7+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 2 \color{blue}{+7} \\\Leftrightarrow &15x & = &9\\\Leftrightarrow & \color{red}{15}x & = &9\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{9}{15} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{+7}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+7}\color{blue}{-7-x } & = & -5 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -5 \color{blue}{-7} \\\Leftrightarrow &-5x & = &-12\\\Leftrightarrow & \color{red}{-5}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-12}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{-1}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-1}\color{blue}{+1-x } & = & 3 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 3 \color{blue}{+1} \\\Leftrightarrow &-5x & = &4\\\Leftrightarrow & \color{red}{-5}x & = &4\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{4}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{-2}& = & 11 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{-2}\color{blue}{+2+9x } & = & 11 \color{red}{ -9x }\color{blue}{+2+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & 11 \color{blue}{+2} \\\Leftrightarrow &14x & = &13\\\Leftrightarrow & \color{red}{14}x & = &13\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{13}{14} \\\Leftrightarrow & \color{green}{ x = \frac{13}{14} } & & \\ & V = \left\{ \frac{13}{14} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{-6}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-6}\color{blue}{+6-x } & = & -11 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -11 \color{blue}{+6} \\\Leftrightarrow &-8x & = &-5\\\Leftrightarrow & \color{red}{-8}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-5}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{-1}& = & 9 \color{red}{ +3x } \\\Leftrightarrow & 11x \color{red}{-1}\color{blue}{+1-3x } & = & 9 \color{red}{ +3x }\color{blue}{+1-3x } \\\Leftrightarrow & 11x \color{blue}{-3x } & = & 9 \color{blue}{+1} \\\Leftrightarrow &8x & = &10\\\Leftrightarrow & \color{red}{8}x & = &10\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{10}{8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{+12}& = & -4 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+12}\color{blue}{-12-x } & = & -4 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -4 \color{blue}{-12} \\\Leftrightarrow &5x & = &-16\\\Leftrightarrow & \color{red}{5}x & = &-16\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-16}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{5} } & & \\ & V = \left\{ \frac{-16}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{-12}& = & 14 \color{red}{ +11x } \\\Leftrightarrow & 9x \color{red}{-12}\color{blue}{+12-11x } & = & 14 \color{red}{ +11x }\color{blue}{+12-11x } \\\Leftrightarrow & 9x \color{blue}{-11x } & = & 14 \color{blue}{+12} \\\Leftrightarrow &-2x & = &26\\\Leftrightarrow & \color{red}{-2}x & = &26\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{26}{-2} \\\Leftrightarrow & \color{green}{ x = -13 } & & \\ & V = \left\{ -13 \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{-8}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-8}\color{blue}{+8-x } & = & 1 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 1 \color{blue}{+8} \\\Leftrightarrow &-3x & = &9\\\Leftrightarrow & \color{red}{-3}x & = &9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{9}{-3} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)