Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{+1}& = & 15 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{+1}\color{blue}{-1+10x } & = & 15 \color{red}{ -10x }\color{blue}{-1+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & 15 \color{blue}{-1} \\\Leftrightarrow &21x & = &14\\\Leftrightarrow & \color{red}{21}x & = &14\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{14}{21} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{+15}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+15}\color{blue}{-15-x } & = & -12 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -12 \color{blue}{-15} \\\Leftrightarrow &5x & = &-27\\\Leftrightarrow & \color{red}{5}x & = &-27\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-27}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{5} } & & \\ & V = \left\{ \frac{-27}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{+1}& = & -5 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{+1}\color{blue}{-1-14x } & = & -5 \color{red}{ +14x }\color{blue}{-1-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & -5 \color{blue}{-1} \\\Leftrightarrow &-25x & = &-6\\\Leftrightarrow & \color{red}{-25}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-6}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{6}{25} } & & \\ & V = \left\{ \frac{6}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{-8}& = & 8 \color{red}{ +6x } \\\Leftrightarrow & 13x \color{red}{-8}\color{blue}{+8-6x } & = & 8 \color{red}{ +6x }\color{blue}{+8-6x } \\\Leftrightarrow & 13x \color{blue}{-6x } & = & 8 \color{blue}{+8} \\\Leftrightarrow &7x & = &16\\\Leftrightarrow & \color{red}{7}x & = &16\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{16}{7} \\\Leftrightarrow & \color{green}{ x = \frac{16}{7} } & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{-2}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-2}\color{blue}{+2-x } & = & 5 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 5 \color{blue}{+2} \\\Leftrightarrow &-15x & = &7\\\Leftrightarrow & \color{red}{-15}x & = &7\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{7}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{15} } & & \\ & V = \left\{ \frac{-7}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{+1}& = & -8 \color{red}{ -2x } \\\Leftrightarrow & 5x \color{red}{+1}\color{blue}{-1+2x } & = & -8 \color{red}{ -2x }\color{blue}{-1+2x } \\\Leftrightarrow & 5x \color{blue}{+2x } & = & -8 \color{blue}{-1} \\\Leftrightarrow &7x & = &-9\\\Leftrightarrow & \color{red}{7}x & = &-9\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-9}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{-13}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-13}\color{blue}{+13-x } & = & -7 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -7 \color{blue}{+13} \\\Leftrightarrow &-12x & = &6\\\Leftrightarrow & \color{red}{-12}x & = &6\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{6}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{-9}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-9}\color{blue}{+9-x } & = & -3 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -3 \color{blue}{+9} \\\Leftrightarrow &x & = &6\\\Leftrightarrow & \color{red}{}x & = &6\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 6 \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{+6}& = & -10 \color{red}{ +10x } \\\Leftrightarrow & x \color{red}{+6}\color{blue}{-6-10x } & = & -10 \color{red}{ +10x }\color{blue}{-6-10x } \\\Leftrightarrow & x \color{blue}{-10x } & = & -10 \color{blue}{-6} \\\Leftrightarrow &-9x & = &-16\\\Leftrightarrow & \color{red}{-9}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-16}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{16}{9} } & & \\ & V = \left\{ \frac{16}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{-3}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{-3}\color{blue}{+3-x } & = & 9 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & 9 \color{blue}{+3} \\\Leftrightarrow &9x & = &12\\\Leftrightarrow & \color{red}{9}x & = &12\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{12}{9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{+5}& = & 7 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{+5}\color{blue}{-5-11x } & = & 7 \color{red}{ +11x }\color{blue}{-5-11x } \\\Leftrightarrow & 8x \color{blue}{-11x } & = & 7 \color{blue}{-5} \\\Leftrightarrow &-3x & = &2\\\Leftrightarrow & \color{red}{-3}x & = &2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{-5}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-5}\color{blue}{+5-13x } & = & -10 \color{red}{ +13x }\color{blue}{+5-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -10 \color{blue}{+5} \\\Leftrightarrow &-19x & = &-5\\\Leftrightarrow & \color{red}{-19}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-5}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{5}{19} } & & \\ & V = \left\{ \frac{5}{19} \right\} & \\\end{align}\)