Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{2}{5})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{60}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{-12} & = & \color{red}{-35x} +6 \\\Leftrightarrow & 60x \color{red}{-12} \color{blue}{+12} \color{blue}{+35x} & = & \color{red}{-35x} +6 \color{blue}{+35x} \color{blue}{+12} \\\Leftrightarrow & 60x+35x& = & 6+12 \\\Leftrightarrow & \color{red}{95} x& = & 18 \\\Leftrightarrow & x = \frac{18}{95} & & \\ & V = \left\{ \frac{18}{95} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{2}{3})& = & 3x+\frac{9}{4} \\\Leftrightarrow & 20x-\frac{10}{3}& = & 3x+\frac{9}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{240}{ \color{blue}{12} }x- \frac{40}{ \color{blue}{12} })& = & (\frac{36}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 240x \color{red}{-40} & = & \color{red}{36x} +27 \\\Leftrightarrow & 240x \color{red}{-40} \color{blue}{+40} \color{blue}{-36x} & = & \color{red}{36x} +27 \color{blue}{-36x} \color{blue}{+40} \\\Leftrightarrow & 240x-36x& = & 27+40 \\\Leftrightarrow & \color{red}{204} x& = & 67 \\\Leftrightarrow & x = \frac{67}{204} & & \\ & V = \left\{ \frac{67}{204} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{3}{7})& = & 7x+\frac{8}{7} \\\Leftrightarrow & -25x+\frac{15}{7}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-175}{ \color{blue}{7} }x+ \frac{15}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -175x \color{red}{+15} & = & \color{red}{49x} +8 \\\Leftrightarrow & -175x \color{red}{+15} \color{blue}{-15} \color{blue}{-49x} & = & \color{red}{49x} +8 \color{blue}{-49x} \color{blue}{-15} \\\Leftrightarrow & -175x-49x& = & 8-15 \\\Leftrightarrow & \color{red}{-224} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{-224} & & \\\Leftrightarrow & x = \frac{1}{32} & & \\ & V = \left\{ \frac{1}{32} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{2}{7})& = & 7x+\frac{4}{5} \\\Leftrightarrow & -10x-\frac{10}{7}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-350}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{-50} & = & \color{red}{245x} +28 \\\Leftrightarrow & -350x \color{red}{-50} \color{blue}{+50} \color{blue}{-245x} & = & \color{red}{245x} +28 \color{blue}{-245x} \color{blue}{+50} \\\Leftrightarrow & -350x-245x& = & 28+50 \\\Leftrightarrow & \color{red}{-595} x& = & 78 \\\Leftrightarrow & x = \frac{78}{-595} & & \\\Leftrightarrow & x = \frac{-78}{595} & & \\ & V = \left\{ \frac{-78}{595} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{3}{5})& = & 7x+\frac{2}{7} \\\Leftrightarrow & -6x+\frac{9}{5}& = & 7x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-210}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{+63} & = & \color{red}{245x} +10 \\\Leftrightarrow & -210x \color{red}{+63} \color{blue}{-63} \color{blue}{-245x} & = & \color{red}{245x} +10 \color{blue}{-245x} \color{blue}{-63} \\\Leftrightarrow & -210x-245x& = & 10-63 \\\Leftrightarrow & \color{red}{-455} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{-455} & & \\\Leftrightarrow & x = \frac{53}{455} & & \\ & V = \left\{ \frac{53}{455} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{4}{3})& = & 5x+\frac{5}{11} \\\Leftrightarrow & 6x-\frac{8}{3}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{198}{ \color{blue}{33} }x- \frac{88}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 198x \color{red}{-88} & = & \color{red}{165x} +15 \\\Leftrightarrow & 198x \color{red}{-88} \color{blue}{+88} \color{blue}{-165x} & = & \color{red}{165x} +15 \color{blue}{-165x} \color{blue}{+88} \\\Leftrightarrow & 198x-165x& = & 15+88 \\\Leftrightarrow & \color{red}{33} x& = & 103 \\\Leftrightarrow & x = \frac{103}{33} & & \\ & V = \left\{ \frac{103}{33} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{3}{11})& = & -5x+\frac{9}{2} \\\Leftrightarrow & 24x+\frac{18}{11}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{528}{ \color{blue}{22} }x+ \frac{36}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 528x \color{red}{+36} & = & \color{red}{-110x} +99 \\\Leftrightarrow & 528x \color{red}{+36} \color{blue}{-36} \color{blue}{+110x} & = & \color{red}{-110x} +99 \color{blue}{+110x} \color{blue}{-36} \\\Leftrightarrow & 528x+110x& = & 99-36 \\\Leftrightarrow & \color{red}{638} x& = & 63 \\\Leftrightarrow & x = \frac{63}{638} & & \\ & V = \left\{ \frac{63}{638} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{5}{8})& = & -7x+\frac{2}{9} \\\Leftrightarrow & -6x+\frac{15}{8}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-432}{ \color{blue}{72} }x+ \frac{135}{ \color{blue}{72} })& = & (\frac{-504}{ \color{blue}{72} }x+ \frac{16}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -432x \color{red}{+135} & = & \color{red}{-504x} +16 \\\Leftrightarrow & -432x \color{red}{+135} \color{blue}{-135} \color{blue}{+504x} & = & \color{red}{-504x} +16 \color{blue}{+504x} \color{blue}{-135} \\\Leftrightarrow & -432x+504x& = & 16-135 \\\Leftrightarrow & \color{red}{72} x& = & -119 \\\Leftrightarrow & x = \frac{-119}{72} & & \\ & V = \left\{ \frac{-119}{72} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{3}{11})& = & 5x+\frac{8}{7} \\\Leftrightarrow & 18x-\frac{18}{11}& = & 5x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1386}{ \color{blue}{77} }x- \frac{126}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1386x \color{red}{-126} & = & \color{red}{385x} +88 \\\Leftrightarrow & 1386x \color{red}{-126} \color{blue}{+126} \color{blue}{-385x} & = & \color{red}{385x} +88 \color{blue}{-385x} \color{blue}{+126} \\\Leftrightarrow & 1386x-385x& = & 88+126 \\\Leftrightarrow & \color{red}{1001} x& = & 214 \\\Leftrightarrow & x = \frac{214}{1001} & & \\ & V = \left\{ \frac{214}{1001} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{3}{5})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 12x-\frac{18}{5}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x- \frac{54}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{-54} & = & \color{red}{75x} +40 \\\Leftrightarrow & 180x \color{red}{-54} \color{blue}{+54} \color{blue}{-75x} & = & \color{red}{75x} +40 \color{blue}{-75x} \color{blue}{+54} \\\Leftrightarrow & 180x-75x& = & 40+54 \\\Leftrightarrow & \color{red}{105} x& = & 94 \\\Leftrightarrow & x = \frac{94}{105} & & \\ & V = \left\{ \frac{94}{105} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{1}{3})& = & -8x+\frac{9}{10} \\\Leftrightarrow & -21x+\frac{7}{3}& = & -8x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-630}{ \color{blue}{30} }x+ \frac{70}{ \color{blue}{30} })& = & (\frac{-240}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -630x \color{red}{+70} & = & \color{red}{-240x} +27 \\\Leftrightarrow & -630x \color{red}{+70} \color{blue}{-70} \color{blue}{+240x} & = & \color{red}{-240x} +27 \color{blue}{+240x} \color{blue}{-70} \\\Leftrightarrow & -630x+240x& = & 27-70 \\\Leftrightarrow & \color{red}{-390} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{-390} & & \\\Leftrightarrow & x = \frac{43}{390} & & \\ & V = \left\{ \frac{43}{390} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{3}{8})& = & -3x+\frac{3}{2} \\\Leftrightarrow & -14x-\frac{21}{8}& = & -3x+\frac{3}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-112}{ \color{blue}{8} }x- \frac{21}{ \color{blue}{8} })& = & (\frac{-24}{ \color{blue}{8} }x+ \frac{12}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -112x \color{red}{-21} & = & \color{red}{-24x} +12 \\\Leftrightarrow & -112x \color{red}{-21} \color{blue}{+21} \color{blue}{+24x} & = & \color{red}{-24x} +12 \color{blue}{+24x} \color{blue}{+21} \\\Leftrightarrow & -112x+24x& = & 12+21 \\\Leftrightarrow & \color{red}{-88} x& = & 33 \\\Leftrightarrow & x = \frac{33}{-88} & & \\\Leftrightarrow & x = \frac{-3}{8} & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)