Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{-6}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-6}\color{blue}{+6-x } & = & -15 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -15 \color{blue}{+6} \\\Leftrightarrow &-3x & = &-9\\\Leftrightarrow & \color{red}{-3}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-9}{-3} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{-3}& = & -13 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-3}\color{blue}{+3+7x } & = & -13 \color{red}{ -7x }\color{blue}{+3+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -13 \color{blue}{+3} \\\Leftrightarrow &15x & = &-10\\\Leftrightarrow & \color{red}{15}x & = &-10\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-10}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{-3}& = & 9 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-3}\color{blue}{+3+7x } & = & 9 \color{red}{ -7x }\color{blue}{+3+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 9 \color{blue}{+3} \\\Leftrightarrow &15x & = &12\\\Leftrightarrow & \color{red}{15}x & = &12\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{12}{15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{+12}& = & -1 \color{red}{ +14x } \\\Leftrightarrow & 5x \color{red}{+12}\color{blue}{-12-14x } & = & -1 \color{red}{ +14x }\color{blue}{-12-14x } \\\Leftrightarrow & 5x \color{blue}{-14x } & = & -1 \color{blue}{-12} \\\Leftrightarrow &-9x & = &-13\\\Leftrightarrow & \color{red}{-9}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-13}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{13}{9} } & & \\ & V = \left\{ \frac{13}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{+4}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+4}\color{blue}{-4-x } & = & 5 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 5 \color{blue}{-4} \\\Leftrightarrow &-6x & = &1\\\Leftrightarrow & \color{red}{-6}x & = &1\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{1}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{+14}& = & -6 \color{red}{ +7x } \\\Leftrightarrow & -2x \color{red}{+14}\color{blue}{-14-7x } & = & -6 \color{red}{ +7x }\color{blue}{-14-7x } \\\Leftrightarrow & -2x \color{blue}{-7x } & = & -6 \color{blue}{-14} \\\Leftrightarrow &-9x & = &-20\\\Leftrightarrow & \color{red}{-9}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-20}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{20}{9} } & & \\ & V = \left\{ \frac{20}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{+5}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+5}\color{blue}{-5-x } & = & -9 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -9 \color{blue}{-5} \\\Leftrightarrow &-16x & = &-14\\\Leftrightarrow & \color{red}{-16}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-14}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{-8}& = & -8 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{-8}\color{blue}{+8-10x } & = & -8 \color{red}{ +10x }\color{blue}{+8-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & -8 \color{blue}{+8} \\\Leftrightarrow &-19x & = &0\\\Leftrightarrow & \color{red}{-19}x & = &0\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{0}{-19} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{-14}& = & -2 \color{red}{ -4x } \\\Leftrightarrow & 13x \color{red}{-14}\color{blue}{+14+4x } & = & -2 \color{red}{ -4x }\color{blue}{+14+4x } \\\Leftrightarrow & 13x \color{blue}{+4x } & = & -2 \color{blue}{+14} \\\Leftrightarrow &17x & = &12\\\Leftrightarrow & \color{red}{17}x & = &12\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{12}{17} \\\Leftrightarrow & \color{green}{ x = \frac{12}{17} } & & \\ & V = \left\{ \frac{12}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{+15}& = & 2 \color{red}{ +4x } \\\Leftrightarrow & 7x \color{red}{+15}\color{blue}{-15-4x } & = & 2 \color{red}{ +4x }\color{blue}{-15-4x } \\\Leftrightarrow & 7x \color{blue}{-4x } & = & 2 \color{blue}{-15} \\\Leftrightarrow &3x & = &-13\\\Leftrightarrow & \color{red}{3}x & = &-13\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-13}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{3} } & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 12x \color{red}{+2}& = & -11 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{+2}\color{blue}{-2-11x } & = & -11 \color{red}{ +11x }\color{blue}{-2-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & -11 \color{blue}{-2} \\\Leftrightarrow &x & = &-13\\\Leftrightarrow & \color{red}{}x & = &-13\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -13 \\\Leftrightarrow & \color{green}{ x = -13 } & & \\ & V = \left\{ -13 \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{-7}& = & 8 \color{red}{ +6x } \\\Leftrightarrow & 5x \color{red}{-7}\color{blue}{+7-6x } & = & 8 \color{red}{ +6x }\color{blue}{+7-6x } \\\Leftrightarrow & 5x \color{blue}{-6x } & = & 8 \color{blue}{+7} \\\Leftrightarrow &-x & = &15\\\Leftrightarrow & \color{red}{-}x & = &15\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{15}{-1} \\\Leftrightarrow & \color{green}{ x = -15 } & & \\ & V = \left\{ -15 \right\} & \\\end{align}\)