Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(3x+10=-15-11x\)
2. \(11x-14=-1+2x\)
3. \(3x+1=6+5x\)
4. \(-8x+12=12+x\)
5. \(-3x+12=-6+7x\)
6. \(15x-3=-7+11x\)
7. \(-x+13=-12+2x\)
8. \(-15x-6=3+x\)
9. \(7x-13=-1+4x\)
10. \(-3x+1=11+x\)
11. \(6x+4=-4-5x\)
12. \(x+6=-3+0x\)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{+10}& = & -15 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{+10}\color{blue}{-10+11x } & = & -15 \color{red}{ -11x }\color{blue}{-10+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & -15 \color{blue}{-10} \\\Leftrightarrow &14x & = &-25\\\Leftrightarrow & \color{red}{14}x & = &-25\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-25}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{14} } & & \\ & V = \left\{ \frac{-25}{14} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{-14}& = & -1 \color{red}{ +2x } \\\Leftrightarrow & 11x \color{red}{-14}\color{blue}{+14-2x } & = & -1 \color{red}{ +2x }\color{blue}{+14-2x } \\\Leftrightarrow & 11x \color{blue}{-2x } & = & -1 \color{blue}{+14} \\\Leftrightarrow &9x & = &13\\\Leftrightarrow & \color{red}{9}x & = &13\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{13}{9} \\\Leftrightarrow & \color{green}{ x = \frac{13}{9} } & & \\ & V = \left\{ \frac{13}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{+1}& = & 6 \color{red}{ +5x } \\\Leftrightarrow & 3x \color{red}{+1}\color{blue}{-1-5x } & = & 6 \color{red}{ +5x }\color{blue}{-1-5x } \\\Leftrightarrow & 3x \color{blue}{-5x } & = & 6 \color{blue}{-1} \\\Leftrightarrow &-2x & = &5\\\Leftrightarrow & \color{red}{-2}x & = &5\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{5}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{+12}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+12}\color{blue}{-12-x } & = & 12 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 12 \color{blue}{-12} \\\Leftrightarrow &-9x & = &0\\\Leftrightarrow & \color{red}{-9}x & = &0\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{0}{-9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{+12}& = & -6 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{+12}\color{blue}{-12-7x } & = & -6 \color{red}{ +7x }\color{blue}{-12-7x } \\\Leftrightarrow & -3x \color{blue}{-7x } & = & -6 \color{blue}{-12} \\\Leftrightarrow &-10x & = &-18\\\Leftrightarrow & \color{red}{-10}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-18}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{-3}& = & -7 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{-3}\color{blue}{+3-11x } & = & -7 \color{red}{ +11x }\color{blue}{+3-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & -7 \color{blue}{+3} \\\Leftrightarrow &4x & = &-4\\\Leftrightarrow & \color{red}{4}x & = &-4\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-4}{4} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{+13}& = & -12 \color{red}{ +2x } \\\Leftrightarrow & -x \color{red}{+13}\color{blue}{-13-2x } & = & -12 \color{red}{ +2x }\color{blue}{-13-2x } \\\Leftrightarrow & -x \color{blue}{-2x } & = & -12 \color{blue}{-13} \\\Leftrightarrow &-3x & = &-25\\\Leftrightarrow & \color{red}{-3}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-25}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{25}{3} } & & \\ & V = \left\{ \frac{25}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{-6}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-6}\color{blue}{+6-x } & = & 3 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 3 \color{blue}{+6} \\\Leftrightarrow &-16x & = &9\\\Leftrightarrow & \color{red}{-16}x & = &9\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{9}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{16} } & & \\ & V = \left\{ \frac{-9}{16} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{-13}& = & -1 \color{red}{ +4x } \\\Leftrightarrow & 7x \color{red}{-13}\color{blue}{+13-4x } & = & -1 \color{red}{ +4x }\color{blue}{+13-4x } \\\Leftrightarrow & 7x \color{blue}{-4x } & = & -1 \color{blue}{+13} \\\Leftrightarrow &3x & = &12\\\Leftrightarrow & \color{red}{3}x & = &12\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{12}{3} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{+1}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+1}\color{blue}{-1-x } & = & 11 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 11 \color{blue}{-1} \\\Leftrightarrow &-4x & = &10\\\Leftrightarrow & \color{red}{-4}x & = &10\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{10}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{+4}& = & -4 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+4}\color{blue}{-4+5x } & = & -4 \color{red}{ -5x }\color{blue}{-4+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & -4 \color{blue}{-4} \\\Leftrightarrow &11x & = &-8\\\Leftrightarrow & \color{red}{11}x & = &-8\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-8}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{11} } & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{+6}& = & -3 \color{red}{ +0x } \\\Leftrightarrow & x \color{red}{+6}\color{blue}{-6+0x } & = & -3 \color{red}{ +0x }\color{blue}{-6+0x } \\\Leftrightarrow & x \color{blue}{+0x } & = & -3 \color{blue}{-6} \\\Leftrightarrow &x & = &-9\\\Leftrightarrow & \color{red}{}x & = &-9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -9 \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)