Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-x+2)& = & 10 \color{red}{+} (-11+x) \\\Leftrightarrow & -3x+6& = &10-11+x \\\Leftrightarrow & -3x \color{red}{+6} & = &-1 \color{red}{+x} \\\Leftrightarrow & -3x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -3x-x& = &-1-6 \\\Leftrightarrow & -4x& = &-7 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{-7}{ \color{red}{-4} } \\\Leftrightarrow & x = \frac{7}{4} & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (6x+5)& = & 6 \color{red}{+} (-4+x) \\\Leftrightarrow & 36x+30& = &6-4+x \\\Leftrightarrow & 36x \color{red}{+30} & = &2 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & 36x-x& = &2-30 \\\Leftrightarrow & 35x& = &-28 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{-28}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{-4}{5} & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-3x+5)& = & -12 \color{red}{-} (-6+x) \\\Leftrightarrow & -9x+15& = &-12+6-x \\\Leftrightarrow & -9x \color{red}{+15} & = &-6 \color{red}{-x} \\\Leftrightarrow & -9x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & -9x+x& = &-6-15 \\\Leftrightarrow & -8x& = &-21 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{-21}{ \color{red}{-8} } \\\Leftrightarrow & x = \frac{21}{8} & & \\ & V = \left\{ \frac{21}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-3x+6)& = & -13 \color{red}{-} (11-5x) \\\Leftrightarrow & -6x+12& = &-13-11+5x \\\Leftrightarrow & -6x \color{red}{+12} & = &-24 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &-24 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & -6x-5x& = &-24-12 \\\Leftrightarrow & -11x& = &-36 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-36}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{36}{11} & & \\ & V = \left\{ \frac{36}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-4x-7)& = & 3 \color{red}{+} (-1+x) \\\Leftrightarrow & -24x-42& = &3-1+x \\\Leftrightarrow & -24x \color{red}{-42} & = &2 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & -24x-x& = &2+42 \\\Leftrightarrow & -25x& = &44 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{44}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-44}{25} & & \\ & V = \left\{ \frac{-44}{25} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-6x+5)& = & -15 \color{red}{-} (10+x) \\\Leftrightarrow & -30x+25& = &-15-10-x \\\Leftrightarrow & -30x \color{red}{+25} & = &-25 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+25} \color{blue}{-25} \color{blue}{+x} & = &-25 \color{red}{-x} \color{blue}{+x} \color{blue}{-25} \\\Leftrightarrow & -30x+x& = &-25-25 \\\Leftrightarrow & -29x& = &-50 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-50}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{50}{29} & & \\ & V = \left\{ \frac{50}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-4x+5)& = & -14 \color{red}{-} (10+x) \\\Leftrightarrow & -12x+15& = &-14-10-x \\\Leftrightarrow & -12x \color{red}{+15} & = &-24 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &-24 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & -12x+x& = &-24-15 \\\Leftrightarrow & -11x& = &-39 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-39}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{39}{11} & & \\ & V = \left\{ \frac{39}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-4x-2)& = & -8 \color{red}{-} (-10+x) \\\Leftrightarrow & -8x-4& = &-8+10-x \\\Leftrightarrow & -8x \color{red}{-4} & = &2 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -8x+x& = &2+4 \\\Leftrightarrow & -7x& = &6 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{6}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-6}{7} & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-6x+6)& = & -6 \color{red}{-} (9-5x) \\\Leftrightarrow & -18x+18& = &-6-9+5x \\\Leftrightarrow & -18x \color{red}{+18} & = &-15 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+18} \color{blue}{-18} \color{blue}{-5x} & = &-15 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-18} \\\Leftrightarrow & -18x-5x& = &-15-18 \\\Leftrightarrow & -23x& = &-33 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-33}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{33}{23} & & \\ & V = \left\{ \frac{33}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-5x+7)& = & -11 \color{red}{+} (12+3x) \\\Leftrightarrow & -10x+14& = &-11+12+3x \\\Leftrightarrow & -10x \color{red}{+14} & = &1 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+14} \color{blue}{-14} \color{blue}{-3x} & = &1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-14} \\\Leftrightarrow & -10x-3x& = &1-14 \\\Leftrightarrow & -13x& = &-13 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-13}{ \color{red}{-13} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (5x-6)& = & 7 \color{red}{-} (-8+x) \\\Leftrightarrow & 20x-24& = &7+8-x \\\Leftrightarrow & 20x \color{red}{-24} & = &15 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 20x+x& = &15+24 \\\Leftrightarrow & 21x& = &39 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{39}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{13}{7} & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-x+4)& = & 11 \color{red}{+} (8+x) \\\Leftrightarrow & -6x+24& = &11+8+x \\\Leftrightarrow & -6x \color{red}{+24} & = &19 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -6x-x& = &19-24 \\\Leftrightarrow & -7x& = &-5 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-5}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{5}{7} & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)