Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{-5}& = & 6 \color{red}{ +7x } \\\Leftrightarrow & 4x \color{red}{-5}\color{blue}{+5-7x } & = & 6 \color{red}{ +7x }\color{blue}{+5-7x } \\\Leftrightarrow & 4x \color{blue}{-7x } & = & 6 \color{blue}{+5} \\\Leftrightarrow &-3x & = &11\\\Leftrightarrow & \color{red}{-3}x & = &11\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{11}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{+8}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+8}\color{blue}{-8-x } & = & -1 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -1 \color{blue}{-8} \\\Leftrightarrow &-14x & = &-9\\\Leftrightarrow & \color{red}{-14}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-9}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{9}{14} } & & \\ & V = \left\{ \frac{9}{14} \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{+3}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+3}\color{blue}{-3-x } & = & -8 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -8 \color{blue}{-3} \\\Leftrightarrow &-15x & = &-11\\\Leftrightarrow & \color{red}{-15}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-11}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{11}{15} } & & \\ & V = \left\{ \frac{11}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{+10}& = & -14 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+10}\color{blue}{-10-13x } & = & -14 \color{red}{ +13x }\color{blue}{-10-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -14 \color{blue}{-10} \\\Leftrightarrow &-28x & = &-24\\\Leftrightarrow & \color{red}{-28}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-24}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{-9}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-9}\color{blue}{+9-x } & = & -10 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -10 \color{blue}{+9} \\\Leftrightarrow &-16x & = &-1\\\Leftrightarrow & \color{red}{-16}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{16} } & & \\ & V = \left\{ \frac{1}{16} \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{-5}& = & 12 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{-5}\color{blue}{+5+7x } & = & 12 \color{red}{ -7x }\color{blue}{+5+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & 12 \color{blue}{+5} \\\Leftrightarrow &22x & = &17\\\Leftrightarrow & \color{red}{22}x & = &17\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{17}{22} \\\Leftrightarrow & \color{green}{ x = \frac{17}{22} } & & \\ & V = \left\{ \frac{17}{22} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{+14}& = & 3 \color{red}{ +9x } \\\Leftrightarrow & 7x \color{red}{+14}\color{blue}{-14-9x } & = & 3 \color{red}{ +9x }\color{blue}{-14-9x } \\\Leftrightarrow & 7x \color{blue}{-9x } & = & 3 \color{blue}{-14} \\\Leftrightarrow &-2x & = &-11\\\Leftrightarrow & \color{red}{-2}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-11}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{11}{2} } & & \\ & V = \left\{ \frac{11}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -3x \color{red}{+15}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+15}\color{blue}{-15-x } & = & 11 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 11 \color{blue}{-15} \\\Leftrightarrow &-4x & = &-4\\\Leftrightarrow & \color{red}{-4}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-4}{-4} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{+15}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+15}\color{blue}{-15-x } & = & 14 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 14 \color{blue}{-15} \\\Leftrightarrow &-4x & = &-1\\\Leftrightarrow & \color{red}{-4}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{-12}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-12}\color{blue}{+12-x } & = & -6 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -6 \color{blue}{+12} \\\Leftrightarrow &-8x & = &6\\\Leftrightarrow & \color{red}{-8}x & = &6\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{6}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{-14}& = & 7 \color{red}{ +10x } \\\Leftrightarrow & -x \color{red}{-14}\color{blue}{+14-10x } & = & 7 \color{red}{ +10x }\color{blue}{+14-10x } \\\Leftrightarrow & -x \color{blue}{-10x } & = & 7 \color{blue}{+14} \\\Leftrightarrow &-11x & = &21\\\Leftrightarrow & \color{red}{-11}x & = &21\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{21}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{11} } & & \\ & V = \left\{ \frac{-21}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{-14}& = & -14 \color{red}{ +4x } \\\Leftrightarrow & 15x \color{red}{-14}\color{blue}{+14-4x } & = & -14 \color{red}{ +4x }\color{blue}{+14-4x } \\\Leftrightarrow & 15x \color{blue}{-4x } & = & -14 \color{blue}{+14} \\\Leftrightarrow &11x & = &0\\\Leftrightarrow & \color{red}{11}x & = &0\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{0}{11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)