solution set
A solution with all real numbers indicates that the equation or inequality has no restrictions on its values, meaning any real number can satisfy it. Graphically, this is often represented as a horizontal line on a number line or as a shaded region extending infinitely in both directions. For example, the equation (x = x) or the inequality (x > -\infty) includes every possible real number as a solution. Essentially, it signifies that the solution set is the entire continuum of real numbers.
The solution to an inequality generally is a region with one more dimension. If the inequality/equation is of the form x < a or x = a then the solution to the inequality is the 1 dimensional line segment while the solution to the equality is a point which has no dimensions. If the inequality/equation is in 2 dimensions, the solution to the inequality is an area whereas the solution to the equality is a 1-d line or curve. And so on, in higher dimensional spaces.
A dotted line in a graph of an inequality indicates that the boundary line is not included in the solution set. This typically occurs with inequalities using "<" or ">", meaning that points on the dotted line do not satisfy the inequality. In contrast, a solid line would indicate that points on the line are included in the solution set, as seen with "<=" or ">=".
If I understand the question correctly, the inequality is not strict. This means that points on the line are part of the solution and so the line is shown as a solid line rather than a dashed line.If I understand the question correctly, the inequality is not strict. This means that points on the line are part of the solution and so the line is shown as a solid line rather than a dashed line.If I understand the question correctly, the inequality is not strict. This means that points on the line are part of the solution and so the line is shown as a solid line rather than a dashed line.If I understand the question correctly, the inequality is not strict. This means that points on the line are part of the solution and so the line is shown as a solid line rather than a dashed line.
solution set
lol
A solution with all real numbers indicates that the equation or inequality has no restrictions on its values, meaning any real number can satisfy it. Graphically, this is often represented as a horizontal line on a number line or as a shaded region extending infinitely in both directions. For example, the equation (x = x) or the inequality (x > -\infty) includes every possible real number as a solution. Essentially, it signifies that the solution set is the entire continuum of real numbers.
The solution to an inequality generally is a region with one more dimension. If the inequality/equation is of the form x < a or x = a then the solution to the inequality is the 1 dimensional line segment while the solution to the equality is a point which has no dimensions. If the inequality/equation is in 2 dimensions, the solution to the inequality is an area whereas the solution to the equality is a 1-d line or curve. And so on, in higher dimensional spaces.
The solution to the inequality 3x < 15 is x < 5. On a number line, this would be represented by an open circle at 5 with an arrow pointing to the left, indicating all real numbers less than 5. The number line would start at negative infinity and end at 5, with 5 not included in the solution set.
An equation has an equal sign, which means that we know what the variable is equal to :)
Any compound inequality, in one variable, can be graphed on the number line.
A dotted line in a graph of an inequality indicates that the boundary line is not included in the solution set. This typically occurs with inequalities using "<" or ">", meaning that points on the dotted line do not satisfy the inequality. In contrast, a solid line would indicate that points on the line are included in the solution set, as seen with "<=" or ">=".
If I understand the question correctly, the inequality is not strict. This means that points on the line are part of the solution and so the line is shown as a solid line rather than a dashed line.If I understand the question correctly, the inequality is not strict. This means that points on the line are part of the solution and so the line is shown as a solid line rather than a dashed line.If I understand the question correctly, the inequality is not strict. This means that points on the line are part of the solution and so the line is shown as a solid line rather than a dashed line.If I understand the question correctly, the inequality is not strict. This means that points on the line are part of the solution and so the line is shown as a solid line rather than a dashed line.
It depends upon the inequality. All points on the line are those which are equal, thus:If the inequality is (strictly) "less than" () then the points on the line are not included; howeverif the inequality is "less than or equals" (≤) or "greater than or equals" (≥) then the points on the line are included.
To determine whether to use a solid or dotted line for a given inequality, check if the inequality includes equal to (≥ or ≤) or not (>) or (<). If it includes equal to, use a solid line; if not, use a dotted line. For the solution area, if the inequality is greater than (>) or greater than or equal to (≥), the solution lies above the line; for less than (<) or less than or equal to (≤), it lies below the line.
The graph of the inequality ( X + 7 ) < 13 is the entire infinite half of the x-y plane to the left of the vertical line ( X = 6 ), but not including the line itself.