Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{5}{3})& = & 2x+\frac{9}{10} \\\Leftrightarrow & -28x-\frac{35}{3}& = & 2x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-840}{ \color{blue}{30} }x- \frac{350}{ \color{blue}{30} })& = & (\frac{60}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -840x \color{red}{-350} & = & \color{red}{60x} +27 \\\Leftrightarrow & -840x \color{red}{-350} \color{blue}{+350} \color{blue}{-60x} & = & \color{red}{60x} +27 \color{blue}{-60x} \color{blue}{+350} \\\Leftrightarrow & -840x-60x& = & 27+350 \\\Leftrightarrow & \color{red}{-900} x& = & 377 \\\Leftrightarrow & x = \frac{377}{-900} & & \\\Leftrightarrow & x = \frac{-377}{900} & & \\ & V = \left\{ \frac{-377}{900} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{3}{8})& = & 9x+\frac{6}{11} \\\Leftrightarrow & 14x+\frac{21}{8}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1232}{ \color{blue}{88} }x+ \frac{231}{ \color{blue}{88} })& = & (\frac{792}{ \color{blue}{88} }x+ \frac{48}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1232x \color{red}{+231} & = & \color{red}{792x} +48 \\\Leftrightarrow & 1232x \color{red}{+231} \color{blue}{-231} \color{blue}{-792x} & = & \color{red}{792x} +48 \color{blue}{-792x} \color{blue}{-231} \\\Leftrightarrow & 1232x-792x& = & 48-231 \\\Leftrightarrow & \color{red}{440} x& = & -183 \\\Leftrightarrow & x = \frac{-183}{440} & & \\ & V = \left\{ \frac{-183}{440} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{3}{11})& = & -9x+\frac{2}{3} \\\Leftrightarrow & 14x-\frac{21}{11}& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{462}{ \color{blue}{33} }x- \frac{63}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 462x \color{red}{-63} & = & \color{red}{-297x} +22 \\\Leftrightarrow & 462x \color{red}{-63} \color{blue}{+63} \color{blue}{+297x} & = & \color{red}{-297x} +22 \color{blue}{+297x} \color{blue}{+63} \\\Leftrightarrow & 462x+297x& = & 22+63 \\\Leftrightarrow & \color{red}{759} x& = & 85 \\\Leftrightarrow & x = \frac{85}{759} & & \\ & V = \left\{ \frac{85}{759} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{3}{5})& = & -7x+\frac{10}{3} \\\Leftrightarrow & 30x-\frac{18}{5}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{450}{ \color{blue}{15} }x- \frac{54}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 450x \color{red}{-54} & = & \color{red}{-105x} +50 \\\Leftrightarrow & 450x \color{red}{-54} \color{blue}{+54} \color{blue}{+105x} & = & \color{red}{-105x} +50 \color{blue}{+105x} \color{blue}{+54} \\\Leftrightarrow & 450x+105x& = & 50+54 \\\Leftrightarrow & \color{red}{555} x& = & 104 \\\Leftrightarrow & x = \frac{104}{555} & & \\ & V = \left\{ \frac{104}{555} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{2}{9})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -16x+\frac{8}{9}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1008}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1008x \color{red}{+56} & = & \color{red}{441x} +90 \\\Leftrightarrow & -1008x \color{red}{+56} \color{blue}{-56} \color{blue}{-441x} & = & \color{red}{441x} +90 \color{blue}{-441x} \color{blue}{-56} \\\Leftrightarrow & -1008x-441x& = & 90-56 \\\Leftrightarrow & \color{red}{-1449} x& = & 34 \\\Leftrightarrow & x = \frac{34}{-1449} & & \\\Leftrightarrow & x = \frac{-34}{1449} & & \\ & V = \left\{ \frac{-34}{1449} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{2}{3})& = & 6x+\frac{7}{5} \\\Leftrightarrow & -25x-\frac{10}{3}& = & 6x+\frac{7}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-375}{ \color{blue}{15} }x- \frac{50}{ \color{blue}{15} })& = & (\frac{90}{ \color{blue}{15} }x+ \frac{21}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -375x \color{red}{-50} & = & \color{red}{90x} +21 \\\Leftrightarrow & -375x \color{red}{-50} \color{blue}{+50} \color{blue}{-90x} & = & \color{red}{90x} +21 \color{blue}{-90x} \color{blue}{+50} \\\Leftrightarrow & -375x-90x& = & 21+50 \\\Leftrightarrow & \color{red}{-465} x& = & 71 \\\Leftrightarrow & x = \frac{71}{-465} & & \\\Leftrightarrow & x = \frac{-71}{465} & & \\ & V = \left\{ \frac{-71}{465} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{2}{11})& = & -9x+\frac{4}{3} \\\Leftrightarrow & 14x-\frac{14}{11}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{462}{ \color{blue}{33} }x- \frac{42}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 462x \color{red}{-42} & = & \color{red}{-297x} +44 \\\Leftrightarrow & 462x \color{red}{-42} \color{blue}{+42} \color{blue}{+297x} & = & \color{red}{-297x} +44 \color{blue}{+297x} \color{blue}{+42} \\\Leftrightarrow & 462x+297x& = & 44+42 \\\Leftrightarrow & \color{red}{759} x& = & 86 \\\Leftrightarrow & x = \frac{86}{759} & & \\ & V = \left\{ \frac{86}{759} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{2}{5})& = & 8x+\frac{4}{9} \\\Leftrightarrow & 21x+\frac{14}{5}& = & 8x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{945}{ \color{blue}{45} }x+ \frac{126}{ \color{blue}{45} })& = & (\frac{360}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 945x \color{red}{+126} & = & \color{red}{360x} +20 \\\Leftrightarrow & 945x \color{red}{+126} \color{blue}{-126} \color{blue}{-360x} & = & \color{red}{360x} +20 \color{blue}{-360x} \color{blue}{-126} \\\Leftrightarrow & 945x-360x& = & 20-126 \\\Leftrightarrow & \color{red}{585} x& = & -106 \\\Leftrightarrow & x = \frac{-106}{585} & & \\ & V = \left\{ \frac{-106}{585} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{4}{11})& = & -9x+\frac{4}{7} \\\Leftrightarrow & -8x+\frac{16}{11}& = & -9x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-616}{ \color{blue}{77} }x+ \frac{112}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -616x \color{red}{+112} & = & \color{red}{-693x} +44 \\\Leftrightarrow & -616x \color{red}{+112} \color{blue}{-112} \color{blue}{+693x} & = & \color{red}{-693x} +44 \color{blue}{+693x} \color{blue}{-112} \\\Leftrightarrow & -616x+693x& = & 44-112 \\\Leftrightarrow & \color{red}{77} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{77} & & \\ & V = \left\{ \frac{-68}{77} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{2}{5})& = & 4x+\frac{6}{5} \\\Leftrightarrow & -15x+\frac{6}{5}& = & 4x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-75}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} })& = & (\frac{20}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -75x \color{red}{+6} & = & \color{red}{20x} +6 \\\Leftrightarrow & -75x \color{red}{+6} \color{blue}{-6} \color{blue}{-20x} & = & \color{red}{20x} +6 \color{blue}{-20x} \color{blue}{-6} \\\Leftrightarrow & -75x-20x& = & 6-6 \\\Leftrightarrow & \color{red}{-95} x& = & 0 \\\Leftrightarrow & x = \frac{0}{-95} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{5}{12})& = & -2x+\frac{8}{9} \\\Leftrightarrow & 15x+\frac{25}{12}& = & -2x+\frac{8}{9} \\ & & & \text{kgv van noemers 12 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{540}{ \color{blue}{36} }x+ \frac{75}{ \color{blue}{36} })& = & (\frac{-72}{ \color{blue}{36} }x+ \frac{32}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 540x \color{red}{+75} & = & \color{red}{-72x} +32 \\\Leftrightarrow & 540x \color{red}{+75} \color{blue}{-75} \color{blue}{+72x} & = & \color{red}{-72x} +32 \color{blue}{+72x} \color{blue}{-75} \\\Leftrightarrow & 540x+72x& = & 32-75 \\\Leftrightarrow & \color{red}{612} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{612} & & \\ & V = \left\{ \frac{-43}{612} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{3}{7})& = & 7x+\frac{9}{5} \\\Leftrightarrow & 20x+\frac{12}{7}& = & 7x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{700}{ \color{blue}{35} }x+ \frac{60}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 700x \color{red}{+60} & = & \color{red}{245x} +63 \\\Leftrightarrow & 700x \color{red}{+60} \color{blue}{-60} \color{blue}{-245x} & = & \color{red}{245x} +63 \color{blue}{-245x} \color{blue}{-60} \\\Leftrightarrow & 700x-245x& = & 63-60 \\\Leftrightarrow & \color{red}{455} x& = & 3 \\\Leftrightarrow & x = \frac{3}{455} & & \\ & V = \left\{ \frac{3}{455} \right\} & \\\end{align}\)