Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

1. \(-2(2x-\frac{4}{9})=9x+\frac{7}{8}\)
2. \(-2(2x-\frac{5}{7})=9x+\frac{6}{11}\)
3. \(-6(4x+\frac{3}{11})=5x+\frac{5}{2}\)
4. \(2(-5x+\frac{4}{9})=7x+\frac{3}{2}\)
5. \(-3(-4x-\frac{5}{4})=5x+\frac{6}{5}\)
6. \(-4(-5x-\frac{2}{9})=7x+\frac{9}{7}\)
7. \(5(-4x-\frac{5}{2})=3x+\frac{4}{9}\)
8. \(-3(-4x+\frac{3}{7})=5x+\frac{6}{11}\)
9. \(2(2x+\frac{2}{3})=3x+\frac{5}{4}\)
10. \(7(3x-\frac{3}{4})=-4x+\frac{10}{7}\)
11. \(7(5x+\frac{5}{9})=-3x+\frac{10}{7}\)
12. \(-3(-5x+\frac{5}{4})=4x+\frac{10}{3}\)

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{4}{9})& = & 9x+\frac{7}{8} \\\Leftrightarrow & -4x+\frac{8}{9}& = & 9x+\frac{7}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-288}{ \color{blue}{72} }x+ \frac{64}{ \color{blue}{72} })& = & (\frac{648}{ \color{blue}{72} }x+ \frac{63}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -288x \color{red}{+64} & = & \color{red}{648x} +63 \\\Leftrightarrow & -288x \color{red}{+64} \color{blue}{-64} \color{blue}{-648x} & = & \color{red}{648x} +63 \color{blue}{-648x} \color{blue}{-64} \\\Leftrightarrow & -288x-648x& = & 63-64 \\\Leftrightarrow & \color{red}{-936} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{-936} & & \\\Leftrightarrow & x = \frac{1}{936} & & \\ & V = \left\{ \frac{1}{936} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{5}{7})& = & 9x+\frac{6}{11} \\\Leftrightarrow & -4x+\frac{10}{7}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-308}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -308x \color{red}{+110} & = & \color{red}{693x} +42 \\\Leftrightarrow & -308x \color{red}{+110} \color{blue}{-110} \color{blue}{-693x} & = & \color{red}{693x} +42 \color{blue}{-693x} \color{blue}{-110} \\\Leftrightarrow & -308x-693x& = & 42-110 \\\Leftrightarrow & \color{red}{-1001} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{-1001} & & \\\Leftrightarrow & x = \frac{68}{1001} & & \\ & V = \left\{ \frac{68}{1001} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{3}{11})& = & 5x+\frac{5}{2} \\\Leftrightarrow & -24x-\frac{18}{11}& = & 5x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-528}{ \color{blue}{22} }x- \frac{36}{ \color{blue}{22} })& = & (\frac{110}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -528x \color{red}{-36} & = & \color{red}{110x} +55 \\\Leftrightarrow & -528x \color{red}{-36} \color{blue}{+36} \color{blue}{-110x} & = & \color{red}{110x} +55 \color{blue}{-110x} \color{blue}{+36} \\\Leftrightarrow & -528x-110x& = & 55+36 \\\Leftrightarrow & \color{red}{-638} x& = & 91 \\\Leftrightarrow & x = \frac{91}{-638} & & \\\Leftrightarrow & x = \frac{-91}{638} & & \\ & V = \left\{ \frac{-91}{638} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{4}{9})& = & 7x+\frac{3}{2} \\\Leftrightarrow & -10x+\frac{8}{9}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-180}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} })& = & (\frac{126}{ \color{blue}{18} }x+ \frac{27}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -180x \color{red}{+16} & = & \color{red}{126x} +27 \\\Leftrightarrow & -180x \color{red}{+16} \color{blue}{-16} \color{blue}{-126x} & = & \color{red}{126x} +27 \color{blue}{-126x} \color{blue}{-16} \\\Leftrightarrow & -180x-126x& = & 27-16 \\\Leftrightarrow & \color{red}{-306} x& = & 11 \\\Leftrightarrow & x = \frac{11}{-306} & & \\\Leftrightarrow & x = \frac{-11}{306} & & \\ & V = \left\{ \frac{-11}{306} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{5}{4})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 12x+\frac{15}{4}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{240}{ \color{blue}{20} }x+ \frac{75}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 240x \color{red}{+75} & = & \color{red}{100x} +24 \\\Leftrightarrow & 240x \color{red}{+75} \color{blue}{-75} \color{blue}{-100x} & = & \color{red}{100x} +24 \color{blue}{-100x} \color{blue}{-75} \\\Leftrightarrow & 240x-100x& = & 24-75 \\\Leftrightarrow & \color{red}{140} x& = & -51 \\\Leftrightarrow & x = \frac{-51}{140} & & \\ & V = \left\{ \frac{-51}{140} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{2}{9})& = & 7x+\frac{9}{7} \\\Leftrightarrow & 20x+\frac{8}{9}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1260}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{81}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1260x \color{red}{+56} & = & \color{red}{441x} +81 \\\Leftrightarrow & 1260x \color{red}{+56} \color{blue}{-56} \color{blue}{-441x} & = & \color{red}{441x} +81 \color{blue}{-441x} \color{blue}{-56} \\\Leftrightarrow & 1260x-441x& = & 81-56 \\\Leftrightarrow & \color{red}{819} x& = & 25 \\\Leftrightarrow & x = \frac{25}{819} & & \\ & V = \left\{ \frac{25}{819} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{5}{2})& = & 3x+\frac{4}{9} \\\Leftrightarrow & -20x-\frac{25}{2}& = & 3x+\frac{4}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-360}{ \color{blue}{18} }x- \frac{225}{ \color{blue}{18} })& = & (\frac{54}{ \color{blue}{18} }x+ \frac{8}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -360x \color{red}{-225} & = & \color{red}{54x} +8 \\\Leftrightarrow & -360x \color{red}{-225} \color{blue}{+225} \color{blue}{-54x} & = & \color{red}{54x} +8 \color{blue}{-54x} \color{blue}{+225} \\\Leftrightarrow & -360x-54x& = & 8+225 \\\Leftrightarrow & \color{red}{-414} x& = & 233 \\\Leftrightarrow & x = \frac{233}{-414} & & \\\Leftrightarrow & x = \frac{-233}{414} & & \\ & V = \left\{ \frac{-233}{414} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{3}{7})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 12x-\frac{9}{7}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x- \frac{99}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{-99} & = & \color{red}{385x} +42 \\\Leftrightarrow & 924x \color{red}{-99} \color{blue}{+99} \color{blue}{-385x} & = & \color{red}{385x} +42 \color{blue}{-385x} \color{blue}{+99} \\\Leftrightarrow & 924x-385x& = & 42+99 \\\Leftrightarrow & \color{red}{539} x& = & 141 \\\Leftrightarrow & x = \frac{141}{539} & & \\ & V = \left\{ \frac{141}{539} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{2}{3})& = & 3x+\frac{5}{4} \\\Leftrightarrow & 4x+\frac{4}{3}& = & 3x+\frac{5}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{48}{ \color{blue}{12} }x+ \frac{16}{ \color{blue}{12} })& = & (\frac{36}{ \color{blue}{12} }x+ \frac{15}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 48x \color{red}{+16} & = & \color{red}{36x} +15 \\\Leftrightarrow & 48x \color{red}{+16} \color{blue}{-16} \color{blue}{-36x} & = & \color{red}{36x} +15 \color{blue}{-36x} \color{blue}{-16} \\\Leftrightarrow & 48x-36x& = & 15-16 \\\Leftrightarrow & \color{red}{12} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{12} & & \\ & V = \left\{ \frac{-1}{12} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{3}{4})& = & -4x+\frac{10}{7} \\\Leftrightarrow & 21x-\frac{21}{4}& = & -4x+\frac{10}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{588}{ \color{blue}{28} }x- \frac{147}{ \color{blue}{28} })& = & (\frac{-112}{ \color{blue}{28} }x+ \frac{40}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 588x \color{red}{-147} & = & \color{red}{-112x} +40 \\\Leftrightarrow & 588x \color{red}{-147} \color{blue}{+147} \color{blue}{+112x} & = & \color{red}{-112x} +40 \color{blue}{+112x} \color{blue}{+147} \\\Leftrightarrow & 588x+112x& = & 40+147 \\\Leftrightarrow & \color{red}{700} x& = & 187 \\\Leftrightarrow & x = \frac{187}{700} & & \\ & V = \left\{ \frac{187}{700} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{5}{9})& = & -3x+\frac{10}{7} \\\Leftrightarrow & 35x+\frac{35}{9}& = & -3x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{2205}{ \color{blue}{63} }x+ \frac{245}{ \color{blue}{63} })& = & (\frac{-189}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 2205x \color{red}{+245} & = & \color{red}{-189x} +90 \\\Leftrightarrow & 2205x \color{red}{+245} \color{blue}{-245} \color{blue}{+189x} & = & \color{red}{-189x} +90 \color{blue}{+189x} \color{blue}{-245} \\\Leftrightarrow & 2205x+189x& = & 90-245 \\\Leftrightarrow & \color{red}{2394} x& = & -155 \\\Leftrightarrow & x = \frac{-155}{2394} & & \\ & V = \left\{ \frac{-155}{2394} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{5}{4})& = & 4x+\frac{10}{3} \\\Leftrightarrow & 15x-\frac{15}{4}& = & 4x+\frac{10}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{180}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{48}{ \color{blue}{12} }x+ \frac{40}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 180x \color{red}{-45} & = & \color{red}{48x} +40 \\\Leftrightarrow & 180x \color{red}{-45} \color{blue}{+45} \color{blue}{-48x} & = & \color{red}{48x} +40 \color{blue}{-48x} \color{blue}{+45} \\\Leftrightarrow & 180x-48x& = & 40+45 \\\Leftrightarrow & \color{red}{132} x& = & 85 \\\Leftrightarrow & x = \frac{85}{132} & & \\ & V = \left\{ \frac{85}{132} \right\} & \\\end{align}\)