Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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