Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-6x-7)& = & -13 \color{red}{+} (13+x) \\\Leftrightarrow & -36x-42& = &-13+13+x \\\Leftrightarrow & -36x \color{red}{-42} & = &0 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & -36x-x& = &0+42 \\\Leftrightarrow & -37x& = &42 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{42}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{-42}{37} & & \\ & V = \left\{ \frac{-42}{37} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-4x+3)& = & 13 \color{red}{-} (6+x) \\\Leftrightarrow & -24x+18& = &13-6-x \\\Leftrightarrow & -24x \color{red}{+18} & = &7 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -24x+x& = &7-18 \\\Leftrightarrow & -23x& = &-11 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-11}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{11}{23} & & \\ & V = \left\{ \frac{11}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (5x+5)& = & -10 \color{red}{+} (-14+x) \\\Leftrightarrow & 20x+20& = &-10-14+x \\\Leftrightarrow & 20x \color{red}{+20} & = &-24 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &-24 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 20x-x& = &-24-20 \\\Leftrightarrow & 19x& = &-44 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-44}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-44}{19} & & \\ & V = \left\{ \frac{-44}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (5x+6)& = & -13 \color{red}{-} (11+x) \\\Leftrightarrow & 20x+24& = &-13-11-x \\\Leftrightarrow & 20x \color{red}{+24} & = &-24 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-24 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 20x+x& = &-24-24 \\\Leftrightarrow & 21x& = &-48 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-48}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-16}{7} & & \\ & V = \left\{ \frac{-16}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-3x-4)& = & 15 \color{red}{-} (1+x) \\\Leftrightarrow & -18x-24& = &15-1-x \\\Leftrightarrow & -18x \color{red}{-24} & = &14 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -18x+x& = &14+24 \\\Leftrightarrow & -17x& = &38 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{38}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-38}{17} & & \\ & V = \left\{ \frac{-38}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (4x-6)& = & 7 \color{red}{+} (15+3x) \\\Leftrightarrow & 20x-30& = &7+15+3x \\\Leftrightarrow & 20x \color{red}{-30} & = &22 \color{red}{+3x} \\\Leftrightarrow & 20x \color{red}{-30} \color{blue}{+30} \color{blue}{-3x} & = &22 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+30} \\\Leftrightarrow & 20x-3x& = &22+30 \\\Leftrightarrow & 17x& = &52 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{52}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{52}{17} & & \\ & V = \left\{ \frac{52}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-2x+7)& = & -15 \color{red}{+} (2+x) \\\Leftrightarrow & -8x+28& = &-15+2+x \\\Leftrightarrow & -8x \color{red}{+28} & = &-13 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & -8x-x& = &-13-28 \\\Leftrightarrow & -9x& = &-41 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-41}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{41}{9} & & \\ & V = \left\{ \frac{41}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-5x+2)& = & -15 \color{red}{+} (-6+x) \\\Leftrightarrow & -25x+10& = &-15-6+x \\\Leftrightarrow & -25x \color{red}{+10} & = &-21 \color{red}{+x} \\\Leftrightarrow & -25x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &-21 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & -25x-x& = &-21-10 \\\Leftrightarrow & -26x& = &-31 \\\Leftrightarrow & \frac{-26x}{ \color{red}{-26} }& = &\frac{-31}{ \color{red}{-26} } \\\Leftrightarrow & x = \frac{31}{26} & & \\ & V = \left\{ \frac{31}{26} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (2x-5)& = & -2 \color{red}{+} (-12+x) \\\Leftrightarrow & 6x-15& = &-2-12+x \\\Leftrightarrow & 6x \color{red}{-15} & = &-14 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & 6x-x& = &-14+15 \\\Leftrightarrow & 5x& = &1 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{1}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{1}{5} & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (2x-6)& = & -11 \color{red}{-} (-1-5x) \\\Leftrightarrow & 8x-24& = &-11+1+5x \\\Leftrightarrow & 8x \color{red}{-24} & = &-10 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{-24} \color{blue}{+24} \color{blue}{-5x} & = &-10 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+24} \\\Leftrightarrow & 8x-5x& = &-10+24 \\\Leftrightarrow & 3x& = &14 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{14}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{14}{3} & & \\ & V = \left\{ \frac{14}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-6x+7)& = & -10 \color{red}{+} (1+x) \\\Leftrightarrow & -30x+35& = &-10+1+x \\\Leftrightarrow & -30x \color{red}{+35} & = &-9 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+35} \color{blue}{-35} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{-35} \\\Leftrightarrow & -30x-x& = &-9-35 \\\Leftrightarrow & -31x& = &-44 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-44}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{44}{31} & & \\ & V = \left\{ \frac{44}{31} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (6x+5)& = & 2 \color{red}{+} (7+x) \\\Leftrightarrow & 24x+20& = &2+7+x \\\Leftrightarrow & 24x \color{red}{+20} & = &9 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 24x-x& = &9-20 \\\Leftrightarrow & 23x& = &-11 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-11}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-11}{23} & & \\ & V = \left\{ \frac{-11}{23} \right\} & \\\end{align}\)