Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-6x-5)& = & 5 \color{red}{-} (13+x) \\\Leftrightarrow & -30x-25& = &5-13-x \\\Leftrightarrow & -30x \color{red}{-25} & = &-8 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-25} \color{blue}{+25} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{+25} \\\Leftrightarrow & -30x+x& = &-8+25 \\\Leftrightarrow & -29x& = &17 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{17}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-17}{29} & & \\ & V = \left\{ \frac{-17}{29} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-6x-6)& = & -4 \color{red}{+} (-1+x) \\\Leftrightarrow & -36x-36& = &-4-1+x \\\Leftrightarrow & -36x \color{red}{-36} & = &-5 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & -36x-x& = &-5+36 \\\Leftrightarrow & -37x& = &31 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{31}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{-31}{37} & & \\ & V = \left\{ \frac{-31}{37} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (3x-4)& = & -10 \color{red}{+} (12-5x) \\\Leftrightarrow & 6x-8& = &-10+12-5x \\\Leftrightarrow & 6x \color{red}{-8} & = &2 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-8} \color{blue}{+8} \color{blue}{+5x} & = &2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+8} \\\Leftrightarrow & 6x+5x& = &2+8 \\\Leftrightarrow & 11x& = &10 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{10}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{10}{11} & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (5x-6)& = & -10 \color{red}{-} (3+x) \\\Leftrightarrow & 20x-24& = &-10-3-x \\\Leftrightarrow & 20x \color{red}{-24} & = &-13 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 20x+x& = &-13+24 \\\Leftrightarrow & 21x& = &11 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{11}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{11}{21} & & \\ & V = \left\{ \frac{11}{21} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-4x-6)& = & 11 \color{red}{-} (10+x) \\\Leftrightarrow & -20x-30& = &11-10-x \\\Leftrightarrow & -20x \color{red}{-30} & = &1 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & -20x+x& = &1+30 \\\Leftrightarrow & -19x& = &31 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{31}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-31}{19} & & \\ & V = \left\{ \frac{-31}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-x-5)& = & -12 \color{red}{+} (-13+x) \\\Leftrightarrow & -2x-10& = &-12-13+x \\\Leftrightarrow & -2x \color{red}{-10} & = &-25 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &-25 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & -2x-x& = &-25+10 \\\Leftrightarrow & -3x& = &-15 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-15}{ \color{red}{-3} } \\\Leftrightarrow & x = 5 & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-x+6)& = & -11 \color{red}{+} (5+3x) \\\Leftrightarrow & -2x+12& = &-11+5+3x \\\Leftrightarrow & -2x \color{red}{+12} & = &-6 \color{red}{+3x} \\\Leftrightarrow & -2x \color{red}{+12} \color{blue}{-12} \color{blue}{-3x} & = &-6 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-12} \\\Leftrightarrow & -2x-3x& = &-6-12 \\\Leftrightarrow & -5x& = &-18 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-18}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{18}{5} & & \\ & V = \left\{ \frac{18}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-x-6)& = & -15 \color{red}{+} (-5-5x) \\\Leftrightarrow & -3x-18& = &-15-5-5x \\\Leftrightarrow & -3x \color{red}{-18} & = &-20 \color{red}{-5x} \\\Leftrightarrow & -3x \color{red}{-18} \color{blue}{+18} \color{blue}{+5x} & = &-20 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+18} \\\Leftrightarrow & -3x+5x& = &-20+18 \\\Leftrightarrow & 2x& = &-2 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{-2}{ \color{red}{2} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (6x+7)& = & -7 \color{red}{+} (-12-5x) \\\Leftrightarrow & 36x+42& = &-7-12-5x \\\Leftrightarrow & 36x \color{red}{+42} & = &-19 \color{red}{-5x} \\\Leftrightarrow & 36x \color{red}{+42} \color{blue}{-42} \color{blue}{+5x} & = &-19 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-42} \\\Leftrightarrow & 36x+5x& = &-19-42 \\\Leftrightarrow & 41x& = &-61 \\\Leftrightarrow & \frac{41x}{ \color{red}{41} }& = &\frac{-61}{ \color{red}{41} } \\\Leftrightarrow & x = \frac{-61}{41} & & \\ & V = \left\{ \frac{-61}{41} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (x+6)& = & -4 \color{red}{-} (13+x) \\\Leftrightarrow & 5x+30& = &-4-13-x \\\Leftrightarrow & 5x \color{red}{+30} & = &-17 \color{red}{-x} \\\Leftrightarrow & 5x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & 5x+x& = &-17-30 \\\Leftrightarrow & 6x& = &-47 \\\Leftrightarrow & \frac{6x}{ \color{red}{6} }& = &\frac{-47}{ \color{red}{6} } \\\Leftrightarrow & x = \frac{-47}{6} & & \\ & V = \left\{ \frac{-47}{6} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-4x+6)& = & -7 \color{red}{+} (14+x) \\\Leftrightarrow & -24x+36& = &-7+14+x \\\Leftrightarrow & -24x \color{red}{+36} & = &7 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & -24x-x& = &7-36 \\\Leftrightarrow & -25x& = &-29 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-29}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{29}{25} & & \\ & V = \left\{ \frac{29}{25} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (3x+1)& = & -2 \color{red}{+} (9+x) \\\Leftrightarrow & 18x+6& = &-2+9+x \\\Leftrightarrow & 18x \color{red}{+6} & = &7 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 18x-x& = &7-6 \\\Leftrightarrow & 17x& = &1 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{1}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{1}{17} & & \\ & V = \left\{ \frac{1}{17} \right\} & \\\end{align}\)